Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
3592 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 3592 conjugacy classes of subgroups — too many to draw. Only its 267 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 | C22×#1010 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#2616 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#5050 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C2×#5047 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #72136 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #69525 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #69522 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #32887 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C22×C3×#41 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#1010 | — | 2 | 12 | no | — |
| 11 | C2×#1010 | — | 2 | 12 | no | — |
| 12 | C22×D3×Q8 | — | 2 | 1 | no | — |
| 13 | C22×#237 | — | 2 | 3 | no | — |
| 14 | C22×#235 | C22 | 1 | 3 | yes | — |
| 15 | C23×Dic6 | C22 | 1 | 3 | yes | — |
| 16 | C2×C3×C22⋊Q8 | C22 | 1 | 3 | yes | — |
| 17 | C22×#216 | C22 | 1 | 3 | yes | — |
| 18 | C22×#215 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×#395 | — | 2 | 1 | no | — |
| 20 | C3×#394 | — | 2 | 3 | no | — |
| 21 | C3×#380 | C22 | 1 | 3 | yes | — |
| 22 | C2×#830 | C22 | 1 | 3 | yes | — |
| 23 | C2×#830 | C22 | 1 | 3 | yes | — |
| 24 | #5050 | — | 2 | 12 | no | — |
| 25 | #5047 | — | 2 | 12 | no | — |
| 26 | C2×#810 | C22 | 1 | 3 | yes | — |
| 27 | C2×#810 | C22 | 1 | 6 | yes | — |
| 28 | C2×#809 | C22 | 1 | 3 | yes | — |
| 29 | C22×2−1+4 | — | 3 | 1 | no | — |
| 30 | C2×#452 | — | 3 | 3 | no | — |
| 31 | C2×#451 | — | 3 | 3 | no | — |
| 32 | #2616 | D3 | 1 | 1 | yes | characteristic, complemented |
| 33 | #1788 | — | 3 | 3 | no | — |
| 34 | #1787 | — | 3 | 3 | no | — |
| 35 | #1780 | — | 3 | 1 | no | — |
| 36 | C2×C3×#41 | — | 2 | 6 | no | — |
| 37 | C2×C3×#41 | — | 2 | 6 | no | — |
| 38 | C22×C3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 39 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 40 | C22×C3×D4 | D4 | 1 | 3 | yes | — |
| 41 | C23×C3×C4 | C23 | 1 | 3 | yes | — |
| 42 | C22×#67 | — | 2 | 3 | no | — |
| 43 | C23×Dic3 | — | 2 | 3 | no | — |
| 44 | #1010 | — | 2 | 32 | no | — |
| 45 | #1010 | — | 2 | 96 | no | — |
| 46 | C2×D3×Q8 | — | 2 | 24 | no | — |
| 47 | C2×#237 | — | 2 | 48 | no | — |
| 48 | C2×#237 | — | 2 | 24 | no | — |
| 49 | C2×#235 | — | 2 | 6 | no | — |
| 50 | C2×#235 | — | 2 | 12 | no | — |
| 51 | C2×#235 | — | 2 | 12 | no | — |
| 52 | C2×#235 | D4 | 1 | 12 | yes | — |
| 53 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 54 | C22×C4×D3 | — | 2 | 3 | no | — |
| 55 | C22×Dic6 | — | 2 | 3 | no | — |
| 56 | C22×Dic6 | — | 2 | 6 | no | — |
| 57 | C22×Dic6 | — | 2 | 12 | no | — |
| 58 | C22×Dic6 | — | 2 | 12 | no | — |
| 59 | C22×Dic6 | D4 | 1 | 12 | yes | — |
| 60 | C22×Dic6 | C23 | 1 | 3 | yes | — |
| 61 | C3×C22⋊Q8 | — | 2 | 6 | no | — |
| 62 | C3×C22⋊Q8 | — | 2 | 6 | no | — |
| 63 | C2×C3×C4⋊C4 | — | 2 | 3 | no | — |
| 64 | C2×C3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 65 | C2×C3×C22⋊C4 | — | 2 | 3 | no | — |
| 66 | C2×C3×C22⋊C4 | — | 2 | 3 | no | — |
| 67 | C2×#216 | — | 2 | 6 | no | — |
| 68 | C2×#216 | — | 2 | 12 | no | — |
| 69 | C2×#215 | — | 2 | 6 | no | — |
| 70 | C22×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 71 | C22×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 72 | C3×#95 | — | 2 | 3 | no | — |
| 73 | #830 | — | 2 | 6 | no | — |
| 74 | #830 | — | 2 | 6 | no | — |
| 75 | #810 | — | 2 | 6 | no | — |
| 76 | #810 | — | 2 | 12 | no | — |
| 77 | #809 | — | 2 | 6 | no | — |
| 78 | C2×2−1+4 | — | 6 | 12 | no | — |
| 79 | C2×2−1+4 | — | 6 | 12 | no | — |
| 80 | C22×#41 | — | 3 | 3 | no | — |
| 81 | C22×#41 | — | 6 | 3 | no | — |
| 82 | C22×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 83 | C23×Q8 | — | 3 | 3 | no | — |
| 84 | C23×Q8 | — | 6 | 1 | no | — |
| 85 | C22×Q16 | — | 3 | 3 | no | — |
| 86 | C22×SD16 | — | 3 | 1 | no | — |
| 87 | C2×C22⋊Q8 | C2×D3 | 1 | 3 | yes | — |
| 88 | #452 | — | 6 | 12 | no | — |
| 89 | #451 | — | 6 | 12 | no | — |
| 90 | C2×#103 | — | 3 | 6 | no | — |
| 91 | C2×#103 | — | 3 | 3 | no | — |
| 92 | C2×#102 | — | 3 | 3 | no | — |
| 93 | C2×C22⋊C8 | — | 3 | 3 | no | — |
| 94 | C2×C22⋊C8 | — | 3 | 3 | no | — |
| 95 | #395 | — | 2 | 1 | no | — |
| 96 | #394 | — | 2 | 3 | no | — |
| 97 | #380 | C2×D3 | 1 | 3 | yes | — |
| 98 | C24×C3 | C2×D4 | 1 | 3 | yes | — |
| 99 | C23×D3 | — | 2 | 1 | no | — |
| 100 | C3×#41 | — | 2 | 8 | no | — |
| 101 | C3×#41 | — | 2 | 24 | no | — |
| 102 | C2×C3×Q8 | — | 2 | 6 | no | — |
| 103 | C2×C3×Q8 | — | 2 | 3 | no | — |
| 104 | C2×C3×Q8 | — | 2 | 3 | no | — |
| 105 | C2×C3×D4 | — | 2 | 12 | no | — |
| 106 | C2×C3×D4 | — | 2 | 6 | no | — |
| 107 | C22×C3×C4 | — | 2 | 6 | no | — |
| 108 | C22×C3×C4 | — | 2 | 6 | no | — |
| 109 | C22×C3×C4 | — | 2 | 3 | no | — |
| 110 | C22×C3×C4 | — | 2 | 1 | no | — |
| 111 | C22×C3×C4 | C2×D4 | 1 | 6 | yes | — |
| 112 | C22×C3×C4 | C2×D4 | 1 | 6 | yes | — |
| 113 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 114 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 115 | C2×#67 | — | 2 | 24 | no | — |
| 116 | C2×#67 | — | 2 | 12 | no | — |
| 117 | C22×Dic3 | — | 2 | 24 | no | — |
| 118 | C22×Dic3 | — | 2 | 12 | no | — |
| 119 | C22×Dic3 | — | 2 | 3 | no | — |
| 120 | D3×Q8 | — | 2 | 64 | no | — |
| 121 | #237 | — | 2 | 192 | no | — |
| 122 | #235 | — | 2 | 48 | no | — |
| 123 | #235 | — | 2 | 24 | no | — |
| 124 | #235 | — | 2 | 24 | no | — |
| 125 | C2×D12 | — | 2 | 3 | no | — |
| 126 | C2×D12 | C2×D4 | 1 | 6 | yes | — |
| 127 | C2×C4×D3 | — | 2 | 24 | no | — |
| 128 | C2×C4×D3 | — | 2 | 12 | no | — |
| 129 | C2×Dic6 | — | 2 | 24 | no | — |
| 130 | C2×Dic6 | — | 2 | 24 | no | — |
| 131 | C2×Dic6 | — | 2 | 24 | no | — |
| 132 | C2×Dic6 | — | 2 | 12 | no | — |
| 133 | C2×Dic6 | — | 2 | 6 | no | — |
| 134 | C2×Dic6 | — | 2 | 3 | no | — |
| 135 | C2×Dic6 | — | 2 | 48 | no | — |
| 136 | C2×Dic6 | C2×D4 | 1 | 6 | yes | — |
| 137 | C2×Dic6 | C2×D4 | 1 | 12 | yes | — |
| 138 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 139 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 140 | C3×C4⋊C4 | — | 4 | 6 | no | — |
| 141 | C3×C22⋊C4 | — | 4 | 6 | no | — |
| 142 | C3×C22⋊C4 | — | 8 | 3 | no | — |
| 143 | #216 | — | 4 | 12 | no | — |
| 144 | #215 | — | 4 | 4 | no | — |
| 145 | C2×C3⋊C8 | — | 2 | 3 | no | — |
| 146 | C2×C3⋊C8 | — | 2 | 3 | no | — |
| 147 | C2×C3⋊C8 | — | 2 | 6 | no | — |
| 148 | 2−1+4 | — | 6 | 96 | no | — |
| 149 | 2−1+4 | — | 6 | 32 | no | — |
| 150 | C2×#41 | — | 2 | 6 | no | — |
| 151 | C2×#41 | — | 2 | 6 | no | — |
| 152 | C2×#41 | — | 3 | 12 | no | — |
| 153 | C2×#41 | — | 6 | 12 | no | — |
| 154 | C2×#41 | — | 6 | 12 | no | — |
| 155 | C2×#41 | — | 6 | 48 | no | — |
| 156 | C2×#41 | — | 6 | 24 | no | — |
| 157 | C2×#41 | — | 6 | 6 | no | — |
| 158 | C22×Q8 | — | 3 | 12 | no | — |
| 159 | C22×Q8 | — | 3 | 3 | no | — |
| 160 | C22×Q8 | — | 6 | 12 | no | — |
| 161 | C22×Q8 | — | 6 | 12 | no | — |
| 162 | C22×Q8 | — | 6 | 24 | no | — |
| 163 | C22×Q8 | — | 6 | 6 | no | — |
| 164 | C22×Q8 | — | 6 | 3 | no | — |
| 165 | C22×Q8 | #67 | 1 | 1 | yes | characteristic |
| 166 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 167 | C22×D4 | — | 3 | 1 | no | — |
| 168 | C22×D4 | — | 6 | 3 | no | — |
| 169 | C22×D4 | #67 | 1 | 3 | yes | — |
| 170 | C23×C4 | — | 6 | 3 | no | — |
| 171 | C23×C4 | — | 6 | 3 | no | — |
| 172 | C23×C4 | C22×D3 | 1 | 3 | yes | — |
| 173 | C2×Q16 | — | 6 | 12 | no | — |
| 174 | C2×Q16 | — | 6 | 6 | no | — |
| 175 | C2×SD16 | — | 6 | 6 | no | — |
| 176 | C22×C8 | — | 3 | 1 | no | — |
| 177 | C22×C8 | — | 3 | 3 | no | — |
| 178 | C22⋊Q8 | — | 2 | 6 | no | — |
| 179 | C22⋊Q8 | — | 2 | 6 | no | — |
| 180 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 181 | C2×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 182 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 183 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 184 | #103 | — | 6 | 12 | no | — |
| 185 | #103 | — | 6 | 6 | no | — |
| 186 | #102 | — | 6 | 6 | no | — |
| 187 | C22⋊C8 | — | 6 | 6 | no | — |
| 188 | C22⋊C8 | — | 6 | 6 | no | — |
| 189 | #95 | — | 2 | 3 | no | — |
| 190 | C23×C3 | — | 2 | 6 | no | — |
| 191 | C23×C3 | — | 2 | 3 | no | — |
| 192 | C23×C3 | — | 2 | 6 | no | — |
| 193 | C23×C3 | — | 2 | 3 | no | — |
| 194 | C23×C3 | #120 | 1 | 6 | yes | — |
| 195 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 196 | C22×D3 | — | 2 | 6 | no | — |
| 197 | C22×D3 | — | 4 | 1 | no | — |
| 198 | C22×D3 | — | 4 | 3 | no | — |
| 199 | C3×Q8 | — | 2 | 8 | no | — |
| 200 | C3×Q8 | — | 4 | 1 | no | — |
| 201 | C3×Q8 | — | 4 | 3 | no | — |
| 202 | C3×D4 | — | 2 | 24 | no | — |
| 203 | C2×C3×C4 | — | 2 | 6 | no | — |
| 204 | C2×C3×C4 | — | 2 | 6 | no | — |
| 205 | C2×C3×C4 | — | 2 | 6 | no | — |
| 206 | C2×C3×C4 | — | 2 | 12 | no | — |
| 207 | C2×C3×C4 | — | 4 | 3 | no | — |
| 208 | C2×C3×C4 | — | 4 | 3 | no | — |
| 209 | C2×C3×C4 | — | 4 | 3 | no | — |
| 210 | C2×C3×C4 | — | 4 | 3 | no | — |
| 211 | C2×C3×C4 | #120 | 1 | 6 | yes | — |
| 212 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 213 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 214 | #67 | — | 2 | 48 | no | — |
| 215 | C2×Dic3 | — | 2 | 48 | no | — |
| 216 | C2×Dic3 | — | 2 | 6 | no | — |
| 217 | C2×Dic3 | — | 2 | 12 | no | — |
| 218 | D12 | — | 2 | 6 | no | — |
| 219 | D12 | #120 | 1 | 4 | yes | — |
| 220 | C4×D3 | — | 2 | 48 | no | — |
| 221 | Dic6 | — | 2 | 48 | no | — |
| 222 | Dic6 | — | 2 | 6 | no | — |
| 223 | Dic6 | — | 2 | 12 | no | — |
| 224 | Dic6 | #120 | 1 | 12 | yes | — |
| 225 | C3⋊C8 | — | 4 | 1 | no | — |
| 226 | C3⋊C8 | — | 4 | 3 | no | — |
| 227 | C24 | — | 6 | 1 | no | — |
| 228 | C24 | C2×#67 | 1 | 3 | yes | — |
| 229 | #41 | — | 2 | 8 | no | — |
| 230 | #41 | — | 2 | 24 | no | — |
| 231 | #41 | — | 6 | 24 | no | — |
| 232 | #41 | — | 6 | 24 | no | — |
| 233 | #41 | — | 6 | 48 | no | — |
| 234 | #41 | — | 6 | 192 | no | — |
| 235 | C2×Q8 | — | 2 | 6 | no | — |
| 236 | C2×Q8 | — | 2 | 3 | no | — |
| 237 | C2×Q8 | — | 2 | 3 | no | — |
| 238 | C2×Q8 | — | 3 | 12 | no | — |
| 239 | C2×Q8 | — | 3 | 6 | no | — |
| 240 | C2×Q8 | — | 6 | 48 | no | — |
| 241 | C2×Q8 | — | 6 | 24 | no | — |
| 242 | C2×Q8 | — | 6 | 24 | no | — |
| 243 | C2×Q8 | — | 6 | 24 | no | — |
| 244 | C2×Q8 | — | 6 | 64 | no | — |
| 245 | C2×Q8 | — | 6 | 12 | no | — |
| 246 | C2×Q8 | — | 6 | 6 | no | — |
| 247 | C2×Q8 | — | 6 | 3 | no | — |
| 248 | C2×D4 | — | 2 | 12 | no | — |
| 249 | C2×D4 | — | 2 | 6 | no | — |
| 250 | C2×D4 | — | 3 | 6 | no | — |
| 251 | C2×D4 | — | 6 | 24 | no | — |
| 252 | C2×D4 | — | 6 | 12 | no | — |
| 253 | C2×D4 | — | 6 | 3 | no | — |
| 254 | C22×C4 | — | 2 | 6 | no | — |
| 255 | C22×C4 | — | 2 | 6 | no | — |
| 256 | C22×C4 | — | 2 | 3 | no | — |
| 257 | C22×C4 | — | 2 | 1 | no | — |
| 258 | C22×C4 | — | 6 | 24 | no | — |
| 259 | C22×C4 | — | 6 | 24 | no | — |
| 260 | C22×C4 | — | 6 | 12 | no | — |
| 261 | C22×C4 | — | 6 | 3 | no | — |
| 262 | C22×C4 | — | 6 | 12 | no | — |
| 263 | C22×C4 | D3×D4 | 1 | 6 | yes | — |
| 264 | C22×C4 | D3×D4 | 1 | 6 | yes | — |
| 265 | C22×C4 | C2×#67 | 1 | 3 | yes | — |
| 266 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 267 | Q16 | — | 12 | 12 | no | — |
| 268 | SD16 | — | 12 | 4 | no | — |
| 269 | C2×C8 | — | 6 | 3 | no | — |
| 270 | C2×C8 | — | 6 | 3 | no | — |
| 271 | C2×C8 | — | 6 | 6 | no | — |
| 272 | C4⋊C4 | — | 2 | 3 | no | — |
| 273 | C4⋊C4 | — | 2 | 3 | no | — |
| 274 | C4⋊C4 | — | 4 | 6 | no | — |
| 275 | C22⋊C4 | — | 4 | 6 | no | — |
| 276 | C22⋊C4 | — | 8 | 3 | no | — |
| 277 | C22×C3 | — | 2 | 6 | no | — |
| 278 | C22×C3 | — | 2 | 6 | no | — |
| 279 | C22×C3 | — | 2 | 6 | no | — |
| 280 | C22×C3 | — | 4 | 6 | no | — |
| 281 | C22×C3 | — | 4 | 6 | no | — |
| 282 | C22×C3 | C2×#120 | 1 | 3 | yes | — |
| 283 | C22×C3 | #577 | 1 | 1 | yes | characteristic |
| 284 | C22×C3 | #578 | 1 | 3 | yes | — |
| 285 | C2×D3 | — | 2 | 4 | no | — |
| 286 | C2×D3 | — | 4 | 6 | no | — |
| 287 | C2×D3 | — | 4 | 6 | no | — |
| 288 | C3×C4 | — | 2 | 6 | no | — |
| 289 | C3×C4 | — | 8 | 1 | no | — |
| 290 | C3×C4 | — | 8 | 3 | no | — |
| 291 | C3×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 292 | C3×C4 | C2×#120 | 1 | 3 | yes | — |
| 293 | Dic3 | — | 2 | 12 | no | — |
| 294 | C23 | — | 2 | 6 | no | — |
| 295 | C23 | — | 2 | 3 | no | — |
| 296 | C23 | — | 2 | 6 | no | — |
| 297 | C23 | — | 2 | 3 | no | — |
| 298 | C23 | — | 6 | 6 | no | — |
| 299 | C23 | — | 12 | 1 | no | — |
| 300 | C23 | — | 12 | 3 | no | — |
| 301 | C23 | #937 | 1 | 6 | yes | — |
| 302 | C23 | C22×#67 | 1 | 1 | yes | characteristic |
| 303 | Q8 | — | 2 | 8 | no | — |
| 304 | Q8 | — | 3 | 12 | no | — |
| 305 | Q8 | — | 4 | 1 | no | — |
| 306 | Q8 | — | 4 | 3 | no | — |
| 307 | Q8 | — | 6 | 48 | no | — |
| 308 | Q8 | — | 6 | 6 | no | — |
| 309 | Q8 | — | 6 | 12 | no | — |
| 310 | D4 | — | 2 | 24 | no | — |
| 311 | D4 | — | 3 | 4 | no | — |
| 312 | D4 | — | 6 | 48 | no | — |
| 313 | D4 | — | 6 | 6 | no | — |
| 314 | C2×C4 | — | 2 | 6 | no | — |
| 315 | C2×C4 | — | 2 | 6 | no | — |
| 316 | C2×C4 | — | 2 | 12 | no | — |
| 317 | C2×C4 | — | 2 | 6 | no | — |
| 318 | C2×C4 | — | 4 | 3 | no | — |
| 319 | C2×C4 | — | 4 | 3 | no | — |
| 320 | C2×C4 | — | 4 | 3 | no | — |
| 321 | C2×C4 | — | 4 | 3 | no | — |
| 322 | C2×C4 | — | 6 | 48 | no | — |
| 323 | C2×C4 | — | 6 | 48 | no | — |
| 324 | C2×C4 | — | 6 | 12 | no | — |
| 325 | C2×C4 | — | 6 | 6 | no | — |
| 326 | C2×C4 | #937 | 1 | 6 | yes | — |
| 327 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 328 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 329 | C8 | — | 12 | 1 | no | — |
| 330 | C8 | — | 12 | 3 | no | — |
| 331 | C2×C3 | — | 4 | 6 | no | — |
| 332 | C2×C3 | #2846 | 1 | 1 | yes | characteristic |
| 333 | C2×C3 | #3011 | 1 | 3 | yes | — |
| 334 | C2×C3 | #3013 | 1 | 3 | yes | — |
| 335 | D3 | — | 4 | 4 | no | — |
| 336 | C22 | — | 2 | 6 | no | — |
| 337 | C22 | — | 2 | 6 | no | — |
| 338 | C22 | — | 2 | 6 | no | — |
| 339 | C22 | — | 4 | 6 | no | — |
| 340 | C22 | — | 4 | 6 | no | — |
| 341 | C22 | — | 6 | 4 | no | — |
| 342 | C22 | — | 12 | 6 | no | — |
| 343 | C22 | — | 12 | 6 | no | — |
| 344 | C22 | C2×#937 | 1 | 3 | yes | — |
| 345 | C22 | #5836 | 1 | 1 | yes | characteristic |
| 346 | C22 | #5838 | 1 | 3 | yes | — |
| 347 | C4 | — | 2 | 6 | no | — |
| 348 | C4 | — | 6 | 12 | no | — |
| 349 | C4 | — | 8 | 1 | no | — |
| 350 | C4 | — | 8 | 3 | no | — |
| 351 | C4 | D3×#120 | 1 | 1 | yes | characteristic |
| 352 | C4 | D3×#120 | 1 | 3 | yes | — |
| 353 | C3 | #32887 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 354 | C2 | — | 4 | 6 | no | — |
| 355 | C2 | — | 12 | 4 | no | — |
| 356 | C2 | #82612 | 1 | 1 | yes | characteristic |
| 357 | C2 | #83411 | 1 | 3 | yes | — |
| 358 | C2 | #83427 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#2616 | C2 | semidirect |
| 3. C2×#5050 | C2 | semidirect |
| 4. C2×#5047 | C2 | semidirect |
| 5. #72136 | C2 | semidirect |
| 6. #69525 | C2 | semidirect |
| 7. #69522 | C2 | semidirect |
| 32. #2616 | D3 | semidirect |
| 353. C3 | #32887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1010 | 2 |
| C3×#2616 | 2 |
| C2×#5050 | 2 |
| C2×#5047 | 2 |
| #72136 | 2 |
| #69525 | 2 |
| #69522 | 2 |
| #32887 | 3 |