Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1916 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 1916 conjugacy classes of subgroups — too many to draw. Only its 225 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D3×#575 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #78662 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C3×#2017 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72121 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #70013 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #68727 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | D3×#338 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #23434 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C2×D3×#41 | C22 | 1 | 3 | yes | — |
| 10 | C3×#575 | C22 | 1 | 3 | yes | complemented |
| 11 | #5822 | C22 | 1 | 6 | yes | complemented |
| 12 | #5777 | — | 2 | 6 | no | — |
| 13 | D3×#137 | — | 2 | 6 | no | — |
| 14 | #5773 | — | 2 | 6 | no | — |
| 15 | D3×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 16 | #5768 | — | 2 | 6 | no | — |
| 17 | D3×#135 | — | 2 | 6 | no | — |
| 18 | #5748 | C22 | 1 | 3 | yes | complemented |
| 19 | C2×D3×M16 | C22 | 1 | 3 | yes | — |
| 20 | C22×ΓL(1,𝔽25) | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×#408 | C22 | 1 | 3 | yes | complemented |
| 22 | #5234 | C22 | 1 | 3 | yes | complemented |
| 23 | #5129 | C22 | 1 | 3 | yes | complemented |
| 24 | #5110 | C22 | 1 | 3 | yes | complemented |
| 25 | #4727 | — | 2 | 6 | no | — |
| 26 | #4726 | — | 2 | 6 | no | — |
| 27 | C3×#338 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C3⋊#338 | C22 | 1 | 3 | yes | complemented |
| 29 | C2×#575 | — | 3 | 3 | no | — |
| 30 | #2879 | — | 3 | 3 | no | — |
| 31 | #2017 | — | 3 | 3 | no | — |
| 32 | #2017 | — | 3 | 1 | no | — |
| 33 | #2017 | — | 3 | 3 | no | — |
| 34 | #2017 | D3 | 1 | 1 | yes | characteristic, complemented |
| 35 | C2×#338 | — | 3 | 1 | no | — |
| 36 | C2×C3×#41 | C23 | 1 | 3 | yes | — |
| 37 | D3×#41 | — | 2 | 6 | no | — |
| 38 | D3×#41 | — | 2 | 6 | no | — |
| 39 | D3×#41 | — | 2 | 6 | no | — |
| 40 | D3×#41 | — | 2 | 6 | no | — |
| 41 | C2×#239 | D4 | 1 | 3 | yes | — |
| 42 | C2×D3×Q8 | D4 | 1 | 3 | yes | — |
| 43 | C2×#237 | — | 2 | 3 | no | — |
| 44 | C2×#237 | D4 | 1 | 3 | yes | — |
| 45 | C2×D3×D4 | — | 2 | 3 | no | — |
| 46 | C2×D3×D4 | D4 | 1 | 3 | yes | — |
| 47 | C2×#235 | — | 2 | 3 | no | — |
| 48 | C2×#235 | C23 | 1 | 3 | yes | — |
| 49 | C22×C4×D3 | — | 2 | 3 | no | — |
| 50 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 51 | C3×#137 | — | 2 | 6 | no | — |
| 52 | C3×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 53 | C3×#135 | — | 2 | 6 | no | — |
| 54 | C2×C3×M16 | C23 | 1 | 3 | yes | — |
| 55 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 56 | #951 | — | 2 | 6 | no | — |
| 57 | #950 | — | 2 | 12 | no | — |
| 58 | #949 | — | 2 | 6 | no | — |
| 59 | #942 | — | 2 | 6 | no | — |
| 60 | #932 | — | 2 | 6 | no | — |
| 61 | C2×#208 | C23 | 1 | 3 | yes | — |
| 62 | C22×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 63 | #919 | — | 2 | 6 | no | — |
| 64 | #918 | — | 2 | 12 | no | — |
| 65 | D3×Q16 | — | 2 | 6 | no | — |
| 66 | #916 | — | 2 | 12 | no | — |
| 67 | #915 | — | 2 | 12 | no | — |
| 68 | #914 | — | 2 | 12 | no | — |
| 69 | D3×SD16 | — | 2 | 12 | no | — |
| 70 | #912 | — | 2 | 6 | no | — |
| 71 | #911 | — | 2 | 12 | no | — |
| 72 | D3×D8 | — | 2 | 6 | no | — |
| 73 | #909 | — | 2 | 6 | no | — |
| 74 | #908 | — | 2 | 6 | no | — |
| 75 | D3×M16 | — | 2 | 6 | no | — |
| 76 | D3×M16 | — | 2 | 6 | no | — |
| 77 | #904 | — | 2 | 6 | no | — |
| 78 | C2×ΓL(1,𝔽25) | — | 2 | 3 | no | — |
| 79 | C2×ΓL(1,𝔽25) | — | 2 | 3 | no | — |
| 80 | C2×ΓL(1,𝔽25) | D4 | 1 | 6 | yes | — |
| 81 | C2×D3×C8 | D4 | 1 | 6 | yes | — |
| 82 | C3×C22⋊C8 | — | 2 | 6 | no | — |
| 83 | #830 | — | 2 | 6 | no | — |
| 84 | (C2×D3)⋊C8 | — | 2 | 6 | no | — |
| 85 | (C2×D3)⋊C8 | — | 2 | 6 | no | — |
| 86 | C22×#41 | — | 3 | 3 | no | — |
| 87 | #575 | — | 3 | 6 | no | — |
| 88 | #575 | — | 3 | 3 | no | — |
| 89 | #575 | — | 6 | 6 | no | — |
| 90 | #575 | — | 6 | 6 | no | — |
| 91 | #575 | — | 6 | 6 | no | — |
| 92 | #575 | C2×D3 | 1 | 3 | yes | complemented |
| 93 | C2×#137 | — | 6 | 6 | no | — |
| 94 | C2×AGL(1,ℤ/8) | — | 6 | 6 | no | — |
| 95 | C2×#135 | — | 6 | 6 | no | — |
| 96 | C22×M16 | — | 3 | 3 | no | — |
| 97 | C22×M16 | — | 3 | 1 | no | — |
| 98 | #408 | — | 3 | 3 | no | — |
| 99 | #408 | — | 3 | 3 | no | — |
| 100 | #408 | — | 3 | 3 | no | — |
| 101 | #408 | — | 6 | 6 | no | — |
| 102 | #408 | C2×D3 | 1 | 3 | yes | complemented |
| 103 | #407 | — | 6 | 6 | no | — |
| 104 | #338 | — | 3 | 3 | no | — |
| 105 | #338 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 106 | C23×D3 | — | 2 | 3 | no | — |
| 107 | C23×D3 | #41 | 1 | 1 | yes | characteristic |
| 108 | C3×#41 | — | 2 | 6 | no | — |
| 109 | C3×#41 | — | 2 | 6 | no | — |
| 110 | C2×C3×Q8 | C2×D4 | 1 | 3 | yes | — |
| 111 | C2×C3×D4 | — | 2 | 3 | no | — |
| 112 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 113 | C22×C3×C4 | — | 2 | 3 | no | — |
| 114 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 115 | C2×#67 | — | 2 | 3 | no | — |
| 116 | C2×#67 | — | 2 | 3 | no | — |
| 117 | C2×#67 | — | 2 | 3 | no | — |
| 118 | C22×Dic3 | — | 2 | 3 | no | — |
| 119 | C22×Dic3 | #41 | 1 | 1 | yes | characteristic |
| 120 | #239 | — | 2 | 6 | no | — |
| 121 | #239 | — | 2 | 6 | no | — |
| 122 | D3×Q8 | — | 2 | 6 | no | — |
| 123 | D3×Q8 | — | 2 | 6 | no | — |
| 124 | #237 | — | 2 | 6 | no | — |
| 125 | #237 | — | 2 | 6 | no | — |
| 126 | #237 | — | 4 | 6 | no | — |
| 127 | #237 | — | 4 | 6 | no | — |
| 128 | D3×D4 | — | 2 | 6 | no | — |
| 129 | D3×D4 | — | 2 | 6 | no | — |
| 130 | D3×D4 | — | 4 | 6 | no | — |
| 131 | D3×D4 | — | 4 | 6 | no | — |
| 132 | #235 | — | 2 | 6 | no | — |
| 133 | #235 | — | 2 | 6 | no | — |
| 134 | #235 | — | 4 | 3 | no | — |
| 135 | #235 | — | 4 | 3 | no | — |
| 136 | #235 | — | 4 | 3 | no | — |
| 137 | #235 | — | 4 | 3 | no | — |
| 138 | C2×D12 | — | 2 | 3 | no | — |
| 139 | C2×D12 | C2×D4 | 1 | 3 | yes | — |
| 140 | C2×C4×D3 | — | 2 | 3 | no | — |
| 141 | C2×C4×D3 | — | 2 | 3 | no | — |
| 142 | C2×C4×D3 | — | 2 | 3 | no | — |
| 143 | C2×C4×D3 | — | 4 | 6 | no | — |
| 144 | C2×C4×D3 | — | 4 | 6 | no | — |
| 145 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 146 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 147 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 148 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 149 | C2×Dic6 | — | 2 | 3 | no | — |
| 150 | C2×Dic6 | C2×D4 | 1 | 3 | yes | — |
| 151 | C3×Q16 | — | 2 | 6 | no | — |
| 152 | C3×SD16 | — | 2 | 12 | no | — |
| 153 | C3×D8 | — | 2 | 6 | no | — |
| 154 | C3×M16 | — | 2 | 6 | no | — |
| 155 | C2×C3×C8 | — | 2 | 3 | no | — |
| 156 | C2×C3×C8 | C2×D4 | 1 | 6 | yes | — |
| 157 | #216 | — | 2 | 12 | no | — |
| 158 | #215 | — | 2 | 12 | no | — |
| 159 | #214 | — | 2 | 12 | no | — |
| 160 | #213 | — | 2 | 12 | no | — |
| 161 | #208 | — | 2 | 6 | no | — |
| 162 | C2×C3⋊C8 | — | 2 | 3 | no | — |
| 163 | C2×C3⋊C8 | C2×D4 | 1 | 6 | yes | — |
| 164 | Dic12 | — | 2 | 6 | no | — |
| 165 | D24 | — | 2 | 6 | no | — |
| 166 | #204 | — | 2 | 12 | no | — |
| 167 | ΓL(1,𝔽25) | — | 2 | 12 | no | — |
| 168 | ΓL(1,𝔽25) | — | 4 | 3 | no | — |
| 169 | ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 170 | D3×C8 | — | 2 | 6 | no | — |
| 171 | D3×C8 | — | 2 | 6 | no | — |
| 172 | C2×#41 | — | 3 | 3 | no | — |
| 173 | C2×#41 | — | 3 | 3 | no | — |
| 174 | C2×#41 | — | 3 | 3 | no | — |
| 175 | C2×#41 | — | 6 | 3 | no | — |
| 176 | C2×#41 | — | 6 | 3 | no | — |
| 177 | C2×#41 | — | 6 | 6 | no | — |
| 178 | C2×#41 | — | 6 | 6 | no | — |
| 179 | C2×#41 | — | 6 | 6 | no | — |
| 180 | C2×#41 | — | 6 | 6 | no | — |
| 181 | C2×#41 | C22×D3 | 1 | 3 | yes | — |
| 182 | C22×Q8 | — | 3 | 3 | no | — |
| 183 | C22×D4 | — | 3 | 3 | no | — |
| 184 | C22×D4 | — | 6 | 3 | no | — |
| 185 | C23×C4 | — | 3 | 1 | no | — |
| 186 | C23×C4 | — | 6 | 3 | no | — |
| 187 | #137 | — | 2 | 6 | no | — |
| 188 | #137 | — | 6 | 6 | no | — |
| 189 | #137 | — | 6 | 12 | no | — |
| 190 | #137 | — | 6 | 12 | no | — |
| 191 | #137 | — | 6 | 6 | no | — |
| 192 | #137 | — | 6 | 6 | no | — |
| 193 | AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 194 | AGL(1,ℤ/8) | — | 6 | 6 | no | — |
| 195 | AGL(1,ℤ/8) | — | 6 | 12 | no | — |
| 196 | AGL(1,ℤ/8) | — | 6 | 12 | no | — |
| 197 | AGL(1,ℤ/8) | — | 6 | 6 | no | — |
| 198 | AGL(1,ℤ/8) | — | 6 | 6 | no | — |
| 199 | #135 | — | 2 | 6 | no | — |
| 200 | #135 | — | 6 | 12 | no | — |
| 201 | #135 | — | 6 | 6 | no | — |
| 202 | #135 | — | 6 | 12 | no | — |
| 203 | #135 | — | 6 | 6 | no | — |
| 204 | #135 | — | 6 | 6 | no | — |
| 205 | C2×Q16 | — | 6 | 6 | no | — |
| 206 | C2×SD16 | — | 6 | 12 | no | — |
| 207 | C2×D8 | — | 6 | 6 | no | — |
| 208 | C2×M16 | — | 3 | 3 | no | — |
| 209 | C2×M16 | — | 3 | 6 | no | — |
| 210 | C2×M16 | — | 6 | 3 | no | — |
| 211 | C2×M16 | — | 6 | 3 | no | — |
| 212 | C2×M16 | — | 6 | 6 | no | — |
| 213 | C2×M16 | — | 6 | 6 | no | — |
| 214 | C2×M16 | C22×D3 | 1 | 3 | yes | — |
| 215 | C22×C8 | — | 3 | 6 | no | — |
| 216 | C22×C8 | — | 3 | 1 | no | — |
| 217 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 218 | C22⋊C8 | — | 2 | 6 | no | — |
| 219 | C22⋊C8 | — | 6 | 6 | no | — |
| 220 | C22⋊C8 | — | 6 | 6 | no | — |
| 221 | C22⋊C8 | — | 6 | 6 | no | — |
| 222 | C23×C3 | — | 2 | 3 | no | — |
| 223 | C23×C3 | C2×#41 | 1 | 1 | yes | characteristic |
| 224 | C22×D3 | — | 2 | 3 | no | — |
| 225 | C22×D3 | — | 4 | 6 | no | — |
| 226 | C22×D3 | — | 8 | 1 | no | — |
| 227 | C22×D3 | — | 8 | 6 | no | — |
| 228 | C22×D3 | #121 | 1 | 3 | yes | — |
| 229 | C22×D3 | #121 | 1 | 3 | yes | — |
| 230 | C3×Q8 | — | 2 | 6 | no | — |
| 231 | C3×D4 | — | 2 | 6 | no | — |
| 232 | C3×D4 | — | 4 | 6 | no | — |
| 233 | C2×C3×C4 | — | 2 | 3 | no | — |
| 234 | C2×C3×C4 | — | 4 | 3 | no | — |
| 235 | C2×C3×C4 | — | 4 | 3 | no | — |
| 236 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 237 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 238 | #67 | — | 4 | 6 | no | — |
| 239 | #67 | — | 4 | 3 | no | — |
| 240 | #67 | — | 4 | 3 | no | — |
| 241 | #67 | — | 4 | 3 | no | — |
| 242 | #67 | — | 4 | 3 | no | — |
| 243 | C2×Dic3 | — | 2 | 3 | no | — |
| 244 | C2×Dic3 | — | 4 | 6 | no | — |
| 245 | C2×Dic3 | #121 | 1 | 3 | yes | — |
| 246 | C2×Dic3 | #121 | 1 | 3 | yes | — |
| 247 | D12 | — | 2 | 6 | no | — |
| 248 | D12 | — | 4 | 3 | no | — |
| 249 | D12 | — | 4 | 3 | no | — |
| 250 | C4×D3 | — | 4 | 6 | no | — |
| 251 | C4×D3 | — | 4 | 3 | no | — |
| 252 | C4×D3 | — | 4 | 3 | no | — |
| 253 | C4×D3 | — | 4 | 6 | no | — |
| 254 | C4×D3 | #120 | 1 | 3 | yes | — |
| 255 | C4×D3 | #120 | 1 | 3 | yes | — |
| 256 | C4×D3 | #120 | 1 | 6 | yes | — |
| 257 | C4×D3 | #127 | 1 | 3 | yes | — |
| 258 | C4×D3 | #127 | 1 | 1 | yes | characteristic |
| 259 | Dic6 | — | 2 | 6 | no | — |
| 260 | Dic6 | — | 4 | 3 | no | — |
| 261 | Dic6 | — | 4 | 3 | no | — |
| 262 | C3×C8 | — | 2 | 6 | no | — |
| 263 | C3×C8 | — | 4 | 1 | no | — |
| 264 | C3⋊C8 | — | 2 | 6 | no | — |
| 265 | C3⋊C8 | — | 4 | 1 | no | — |
| 266 | C24 | — | 3 | 1 | no | — |
| 267 | C24 | — | 6 | 3 | no | — |
| 268 | #41 | — | 2 | 6 | no | — |
| 269 | #41 | — | 2 | 6 | no | — |
| 270 | #41 | — | 6 | 6 | no | — |
| 271 | #41 | — | 6 | 6 | no | — |
| 272 | #41 | — | 6 | 6 | no | — |
| 273 | #41 | — | 6 | 6 | no | — |
| 274 | #41 | — | 6 | 6 | no | — |
| 275 | #41 | — | 6 | 6 | no | — |
| 276 | #41 | — | 12 | 3 | no | — |
| 277 | #41 | — | 12 | 3 | no | — |
| 278 | #41 | — | 12 | 3 | no | — |
| 279 | #41 | — | 12 | 3 | no | — |
| 280 | #41 | — | 12 | 6 | no | — |
| 281 | #41 | — | 12 | 6 | no | — |
| 282 | C2×Q8 | — | 3 | 3 | no | — |
| 283 | C2×Q8 | — | 6 | 3 | no | — |
| 284 | C2×Q8 | — | 6 | 6 | no | — |
| 285 | C2×Q8 | — | 6 | 6 | no | — |
| 286 | C2×Q8 | D3×D4 | 1 | 3 | yes | — |
| 287 | C2×D4 | — | 2 | 3 | no | — |
| 288 | C2×D4 | — | 3 | 3 | no | — |
| 289 | C2×D4 | — | 6 | 3 | no | — |
| 290 | C2×D4 | — | 6 | 6 | no | — |
| 291 | C2×D4 | — | 6 | 6 | no | — |
| 292 | C2×D4 | — | 6 | 3 | no | — |
| 293 | C2×D4 | — | 6 | 3 | no | — |
| 294 | C2×D4 | — | 6 | 3 | no | — |
| 295 | C2×D4 | — | 12 | 6 | no | — |
| 296 | C2×D4 | — | 12 | 6 | no | — |
| 297 | C2×D4 | D3×D4 | 1 | 3 | yes | — |
| 298 | C22×C4 | — | 2 | 3 | no | — |
| 299 | C22×C4 | — | 3 | 1 | no | — |
| 300 | C22×C4 | — | 3 | 3 | no | — |
| 301 | C22×C4 | — | 3 | 3 | no | — |
| 302 | C22×C4 | — | 3 | 3 | no | — |
| 303 | C22×C4 | — | 3 | 3 | no | — |
| 304 | C22×C4 | — | 6 | 3 | no | — |
| 305 | C22×C4 | — | 6 | 3 | no | — |
| 306 | C22×C4 | — | 6 | 3 | no | — |
| 307 | C22×C4 | — | 6 | 3 | no | — |
| 308 | C22×C4 | — | 12 | 6 | no | — |
| 309 | C22×C4 | — | 12 | 6 | no | — |
| 310 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 311 | Q16 | — | 2 | 6 | no | — |
| 312 | Q16 | — | 6 | 6 | no | — |
| 313 | Q16 | — | 6 | 12 | no | — |
| 314 | SD16 | — | 2 | 12 | no | — |
| 315 | SD16 | — | 6 | 12 | no | — |
| 316 | SD16 | — | 6 | 12 | no | — |
| 317 | SD16 | — | 6 | 12 | no | — |
| 318 | D8 | — | 2 | 6 | no | — |
| 319 | D8 | — | 6 | 6 | no | — |
| 320 | D8 | — | 6 | 12 | no | — |
| 321 | M16 | — | 2 | 6 | no | — |
| 322 | M16 | — | 6 | 12 | no | — |
| 323 | M16 | — | 6 | 6 | no | — |
| 324 | M16 | — | 12 | 3 | no | — |
| 325 | M16 | — | 12 | 1 | no | — |
| 326 | C2×C8 | — | 2 | 3 | no | — |
| 327 | C2×C8 | — | 3 | 6 | no | — |
| 328 | C2×C8 | — | 6 | 6 | no | — |
| 329 | C2×C8 | — | 6 | 6 | no | — |
| 330 | C2×C8 | — | 6 | 3 | no | — |
| 331 | C2×C8 | D3×D4 | 1 | 6 | yes | — |
| 332 | C22×C3 | — | 4 | 1 | no | — |
| 333 | C22×C3 | — | 4 | 6 | no | — |
| 334 | C22×C3 | — | 4 | 3 | no | — |
| 335 | C22×C3 | C2×#121 | 1 | 3 | yes | — |
| 336 | C2×D3 | — | 4 | 3 | no | — |
| 337 | C2×D3 | — | 4 | 3 | no | — |
| 338 | C2×D3 | — | 4 | 6 | no | — |
| 339 | C2×D3 | — | 4 | 3 | no | — |
| 340 | C2×D3 | — | 8 | 12 | no | — |
| 341 | C2×D3 | #392 | 1 | 3 | yes | — |
| 342 | C2×D3 | #392 | 1 | 1 | yes | characteristic |
| 343 | C3×C4 | — | 4 | 3 | no | — |
| 344 | C3×C4 | C2×#120 | 1 | 3 | yes | — |
| 345 | C3×C4 | C2×#127 | 1 | 1 | yes | characteristic |
| 346 | Dic3 | — | 4 | 3 | no | — |
| 347 | Dic3 | #392 | 1 | 1 | yes | characteristic |
| 348 | Dic3 | #392 | 1 | 3 | yes | — |
| 349 | C23 | — | 2 | 3 | no | — |
| 350 | C23 | — | 3 | 3 | no | — |
| 351 | C23 | — | 3 | 3 | no | — |
| 352 | C23 | — | 6 | 3 | no | — |
| 353 | C23 | — | 12 | 6 | no | — |
| 354 | C23 | — | 24 | 1 | no | — |
| 355 | C23 | — | 24 | 6 | no | — |
| 356 | C23 | D3×#41 | 1 | 1 | yes | characteristic |
| 357 | Q8 | — | 2 | 6 | no | — |
| 358 | Q8 | — | 6 | 6 | no | — |
| 359 | Q8 | — | 12 | 3 | no | — |
| 360 | Q8 | — | 12 | 3 | no | — |
| 361 | D4 | — | 2 | 6 | no | — |
| 362 | D4 | — | 4 | 6 | no | — |
| 363 | D4 | — | 6 | 6 | no | — |
| 364 | D4 | — | 12 | 3 | no | — |
| 365 | D4 | — | 12 | 3 | no | — |
| 366 | D4 | — | 12 | 3 | no | — |
| 367 | D4 | — | 12 | 3 | no | — |
| 368 | D4 | — | 12 | 3 | no | — |
| 369 | D4 | — | 12 | 3 | no | — |
| 370 | D4 | — | 12 | 6 | no | — |
| 371 | C2×C4 | — | 2 | 3 | no | — |
| 372 | C2×C4 | — | 3 | 3 | no | — |
| 373 | C2×C4 | — | 3 | 3 | no | — |
| 374 | C2×C4 | — | 3 | 3 | no | — |
| 375 | C2×C4 | — | 3 | 1 | no | — |
| 376 | C2×C4 | — | 3 | 3 | no | — |
| 377 | C2×C4 | — | 3 | 3 | no | — |
| 378 | C2×C4 | — | 3 | 6 | no | — |
| 379 | C2×C4 | — | 4 | 3 | no | — |
| 380 | C2×C4 | — | 4 | 3 | no | — |
| 381 | C2×C4 | — | 6 | 3 | no | — |
| 382 | C2×C4 | — | 12 | 6 | no | — |
| 383 | C2×C4 | — | 12 | 6 | no | — |
| 384 | C2×C4 | — | 12 | 6 | no | — |
| 385 | C2×C4 | — | 12 | 3 | no | — |
| 386 | C2×C4 | — | 12 | 3 | no | — |
| 387 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 388 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 389 | C8 | — | 2 | 6 | no | — |
| 390 | C8 | — | 4 | 1 | no | — |
| 391 | C8 | — | 6 | 6 | no | — |
| 392 | C8 | — | 12 | 1 | no | — |
| 393 | C2×C3 | — | 2 | 3 | no | — |
| 394 | C2×C3 | — | 8 | 3 | no | — |
| 395 | C2×C3 | C2×#392 | 1 | 1 | yes | characteristic |
| 396 | D3 | — | 2 | 3 | no | — |
| 397 | D3 | — | 2 | 1 | no | — |
| 398 | D3 | — | 8 | 3 | no | — |
| 399 | C22 | — | 3 | 3 | no | — |
| 400 | C22 | — | 3 | 1 | no | — |
| 401 | C22 | — | 4 | 1 | no | — |
| 402 | C22 | — | 4 | 6 | no | — |
| 403 | C22 | — | 4 | 3 | no | — |
| 404 | C22 | — | 12 | 3 | no | — |
| 405 | C22 | — | 12 | 3 | no | — |
| 406 | C22 | — | 12 | 6 | no | — |
| 407 | C22 | — | 12 | 3 | no | — |
| 408 | C22 | — | 24 | 12 | no | — |
| 409 | C22 | D3×#121 | 1 | 3 | yes | — |
| 410 | C4 | — | 3 | 3 | no | — |
| 411 | C4 | — | 3 | 1 | no | — |
| 412 | C4 | — | 4 | 3 | no | — |
| 413 | C4 | — | 12 | 3 | no | — |
| 414 | C4 | D3×#120 | 1 | 3 | yes | — |
| 415 | C4 | D3×#127 | 1 | 1 | yes | characteristic |
| 416 | C3 | #23434 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 417 | C2 | — | 2 | 3 | no | — |
| 418 | C2 | — | 6 | 3 | no | — |
| 419 | C2 | — | 6 | 1 | no | — |
| 420 | C2 | — | 8 | 3 | no | — |
| 421 | C2 | — | 24 | 3 | no | — |
| 422 | C2 | D3×#392 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D3×#575 | C2 | semidirect |
| 2. #78662 | C2 | semidirect |
| 3. C3×#2017 | C2 | semidirect |
| 4. #72121 | C2 | semidirect |
| 5. #70013 | C2 | semidirect |
| 6. #68727 | C2 | semidirect |
| 7. D3×#338 | C2 | semidirect |
| 10. C3×#575 | C22 | semidirect |
| 11. #5822 | C22 | semidirect |
| 18. #5748 | C22 | semidirect |
| 21. C3×#408 | C22 | semidirect |
| 22. #5234 | C22 | semidirect |
| 23. #5129 | C22 | semidirect |
| 24. #5110 | C22 | semidirect |
| 27. C3×#338 | C22 | semidirect |
| 28. C3⋊#338 | C22 | semidirect |
| 34. #2017 | D3 | semidirect |
| 92. #575 | C2×D3 | semidirect |
| 102. #408 | C2×D3 | semidirect |
| 105. #338 | C2×D3 | semidirect |
| 416. C3 | #23434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#575 | 2 |
| #78662 | 2 |
| C3×#2017 | 2 |
| #72121 | 2 |
| #70013 | 2 |
| #68727 | 2 |
| D3×#338 | 2 |
| #23434 | 3 |