Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1382 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 177 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 | C2×#5924 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4×#994 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #85528 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #85364 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #85360 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C4×#985 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C4×#984 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C4×#577 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C2×#994 | C22 | 1 | 1 | yes | characteristic |
| 10 | #5924 | C4 | 1 | 8 | yes | direct product factor |
| 11 | C2×#985 | C22 | 1 | 3 | yes | — |
| 12 | C2×#984 | C22 | 1 | 3 | yes | — |
| 13 | C4×D3×Q8 | — | 4 | 1 | no | maximal |
| 14 | #520⋊C3 | C22 | 1 | 3 | yes | — |
| 15 | C4×#41⋊C3 | C22 | 1 | 3 | yes | — |
| 16 | #5426 | C22 | 1 | 3 | yes | — |
| 17 | #5424 | C22 | 1 | 3 | yes | — |
| 18 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C4×GL(2,𝔽3) | C22 | 1 | 3 | yes | complemented |
| 20 | #5388 | C22 | 1 | 6 | yes | complemented |
| 21 | C4×#226 | C22 | 1 | 3 | yes | complemented |
| 22 | C4×#226 | C22 | 1 | 3 | yes | complemented |
| 23 | C2×#577 | — | 3 | 1 | no | — |
| 24 | C4×2−1+4 | — | 3 | 1 | no | — |
| 25 | C4×H(5,𝔽2) | D3 | 1 | 1 | yes | characteristic, complemented |
| 26 | #2952 | — | 3 | 3 | no | — |
| 27 | #2949 | — | 3 | 3 | no | — |
| 28 | #2947 | — | 3 | 3 | no | — |
| 29 | #2946 | — | 3 | 3 | no | — |
| 30 | C4×#137 | — | 3 | 3 | no | — |
| 31 | C4×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 32 | C4×#135 | — | 3 | 3 | no | — |
| 33 | C2×C4×SD16 | — | 3 | 3 | no | — |
| 34 | #2912 | — | 3 | 1 | no | — |
| 35 | #2898 | — | 3 | 1 | no | — |
| 36 | #2897 | — | 3 | 1 | no | — |
| 37 | C4×#131 | — | 3 | 1 | no | — |
| 38 | C2×D3×Q8 | — | 4 | 1 | no | — |
| 39 | #994 | C2×C4 | 1 | 4 | yes | complemented |
| 40 | C2×#41⋊C3 | C23 | 1 | 3 | yes | — |
| 41 | #985 | C2×C4 | 1 | 12 | yes | complemented |
| 42 | #984 | C2×C4 | 1 | 12 | yes | complemented |
| 43 | C2×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 44 | C2×#226 | C23 | 1 | 3 | yes | — |
| 45 | C3×C4×Q8 | — | 4 | 1 | no | — |
| 46 | Q8×Dic3 | — | 4 | 1 | no | — |
| 47 | D3×C4⋊C4 | — | 4 | 3 | no | — |
| 48 | #887 | — | 4 | 3 | no | — |
| 49 | C42×D3 | — | 4 | 3 | no | — |
| 50 | C4×Dic6 | — | 4 | 3 | no | — |
| 51 | C4×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 52 | C4×SL(2,𝔽3) | C23 | 1 | 3 | yes | — |
| 53 | #859 | C23 | 1 | 1 | yes | characteristic |
| 54 | #859 | C23 | 1 | 3 | yes | — |
| 55 | C2×2−1+4 | — | 3 | 1 | no | — |
| 56 | C2×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 57 | #577 | — | 3 | 8 | no | — |
| 58 | #577 | — | 3 | 8 | no | — |
| 59 | C2×#137 | — | 3 | 3 | no | — |
| 60 | C2×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 61 | C2×#135 | — | 3 | 3 | no | — |
| 62 | C22×SD16 | — | 3 | 3 | no | — |
| 63 | C2×#131 | — | 3 | 1 | no | — |
| 64 | C2×#131 | — | 3 | 1 | no | — |
| 65 | #520 | — | 3 | 1 | no | — |
| 66 | #520 | — | 3 | 1 | no | — |
| 67 | #520 | — | 3 | 3 | no | — |
| 68 | #520 | — | 6 | 3 | no | — |
| 69 | #520 | C2×D3 | 1 | 3 | yes | — |
| 70 | #519 | — | 3 | 3 | no | — |
| 71 | #519 | — | 6 | 1 | no | — |
| 72 | #518 | — | 3 | 3 | no | — |
| 73 | C4×#41 | — | 3 | 1 | no | — |
| 74 | C4×#41 | — | 3 | 3 | no | — |
| 75 | C4×#41 | — | 6 | 3 | no | — |
| 76 | C4×#41 | C2×D3 | 1 | 3 | yes | — |
| 77 | C2×C4×Q8 | — | 3 | 3 | no | — |
| 78 | C2×C4×Q8 | — | 6 | 1 | no | — |
| 79 | C2×C4×D4 | — | 3 | 3 | no | — |
| 80 | #442 | — | 3 | 6 | no | — |
| 81 | #441 | — | 3 | 6 | no | — |
| 82 | #440 | — | 3 | 6 | no | — |
| 83 | #440 | — | 3 | 6 | no | — |
| 84 | C4×Q16 | — | 3 | 3 | no | — |
| 85 | C4×Q16 | — | 3 | 3 | no | — |
| 86 | C4×SD16 | — | 3 | 3 | no | — |
| 87 | C4×SD16 | — | 3 | 6 | no | — |
| 88 | C4×SD16 | — | 3 | 6 | no | — |
| 89 | C4×SD16 | — | 3 | 6 | no | — |
| 90 | C4×SD16 | — | 3 | 3 | no | — |
| 91 | C4×SD16 | — | 3 | 1 | no | — |
| 92 | C4×SD16 | — | 3 | 3 | no | — |
| 93 | C4×D8 | — | 3 | 3 | no | — |
| 94 | C4×D8 | — | 3 | 3 | no | — |
| 95 | #428 | — | 3 | 3 | no | — |
| 96 | #428 | — | 3 | 3 | no | — |
| 97 | #427 | — | 3 | 3 | no | — |
| 98 | C2×#106 | — | 3 | 3 | no | — |
| 99 | #419 | — | 3 | 3 | no | — |
| 100 | #418 | — | 3 | 3 | no | — |
| 101 | #417 | — | 3 | 3 | no | — |
| 102 | #417 | — | 3 | 3 | no | — |
| 103 | #416 | — | 3 | 3 | no | — |
| 104 | #416 | — | 3 | 3 | no | — |
| 105 | C2×#103 | — | 3 | 3 | no | — |
| 106 | C2×#102 | — | 3 | 3 | no | — |
| 107 | #405 | — | 3 | 3 | no | — |
| 108 | #405 | — | 3 | 3 | no | — |
| 109 | C4×M16 | — | 3 | 3 | no | — |
| 110 | C2×C4×C8 | — | 3 | 3 | no | — |
| 111 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 112 | D3×Q8 | — | 4 | 8 | no | — |
| 113 | C2×C4×D3 | — | 4 | 1 | no | — |
| 114 | C2×C4×D3 | — | 4 | 3 | no | — |
| 115 | C2×C4×D3 | — | 4 | 3 | no | — |
| 116 | C2×Dic6 | — | 4 | 3 | no | — |
| 117 | #41⋊C3 | C22×C4 | 1 | 6 | yes | — |
| 118 | C2×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 119 | GL(2,𝔽3) | C22×C4 | 1 | 2 | yes | complemented |
| 120 | #226 | C22×C4 | 1 | 6 | yes | complemented |
| 121 | C3×C4⋊C4 | — | 4 | 3 | no | — |
| 122 | C3×C42 | — | 4 | 3 | no | — |
| 123 | C4⋊Dic3 | — | 4 | 3 | no | — |
| 124 | Dic3⋊C4 | — | 4 | 6 | no | — |
| 125 | C4×Dic3 | — | 4 | 3 | no | — |
| 126 | C4×Dic3 | — | 4 | 3 | no | — |
| 127 | C4×Dic3 | — | 4 | 3 | no | — |
| 128 | 2−1+4 | — | 3 | 8 | no | — |
| 129 | 2−1+4 | — | 6 | 4 | no | — |
| 130 | H(5,𝔽2) | — | 3 | 4 | no | — |
| 131 | H(5,𝔽2) | C4×D3 | 1 | 4 | yes | complemented |
| 132 | C2×#41 | — | 3 | 1 | no | — |
| 133 | C2×#41 | — | 3 | 3 | no | — |
| 134 | C2×#41 | — | 6 | 3 | no | — |
| 135 | C2×#41 | C22×D3 | 1 | 3 | yes | — |
| 136 | C22×Q8 | — | 3 | 3 | no | — |
| 137 | C22×Q8 | — | 6 | 1 | no | — |
| 138 | C22×D4 | — | 3 | 3 | no | — |
| 139 | C23×C4 | — | 6 | 1 | no | — |
| 140 | #137 | — | 3 | 12 | no | — |
| 141 | #137 | — | 3 | 12 | no | — |
| 142 | AGL(1,ℤ/8) | — | 3 | 24 | no | — |
| 143 | #135 | — | 3 | 12 | no | — |
| 144 | #135 | — | 3 | 12 | no | — |
| 145 | C2×Q16 | — | 3 | 3 | no | — |
| 146 | C2×SD16 | — | 3 | 3 | no | — |
| 147 | C2×SD16 | — | 3 | 6 | no | — |
| 148 | C2×SD16 | — | 3 | 24 | no | — |
| 149 | C2×SD16 | — | 3 | 1 | no | — |
| 150 | C2×D8 | — | 3 | 3 | no | — |
| 151 | #131 | — | 3 | 8 | no | — |
| 152 | #131 | — | 6 | 4 | no | — |
| 153 | C2×M16 | — | 3 | 3 | no | — |
| 154 | C2×M16 | — | 3 | 3 | no | — |
| 155 | C22×C8 | — | 3 | 3 | no | — |
| 156 | C22×C8 | — | 3 | 3 | no | — |
| 157 | C4×Q8 | — | 3 | 1 | no | — |
| 158 | C4×Q8 | — | 3 | 3 | no | — |
| 159 | C4×Q8 | — | 3 | 6 | no | — |
| 160 | C4×Q8 | — | 3 | 3 | no | — |
| 161 | C4×Q8 | — | 6 | 3 | no | — |
| 162 | C4×Q8 | — | 6 | 3 | no | — |
| 163 | C4×Q8 | — | 6 | 1 | no | — |
| 164 | C4×Q8 | — | 6 | 3 | no | — |
| 165 | C4×Q8 | — | 6 | 3 | no | — |
| 166 | C4×Q8 | S4 | 1 | 1 | yes | characteristic |
| 167 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 168 | C4×Q8 | C22×D3 | 1 | 3 | yes | — |
| 169 | C4×D4 | — | 3 | 3 | no | — |
| 170 | C4×D4 | — | 3 | 6 | no | — |
| 171 | C4×D4 | — | 3 | 3 | no | — |
| 172 | C4×D4 | — | 3 | 3 | no | — |
| 173 | C4×D4 | — | 3 | 1 | no | — |
| 174 | C4×D4 | — | 3 | 3 | no | — |
| 175 | C4×D4 | — | 3 | 3 | no | — |
| 176 | C4×D4 | — | 6 | 3 | no | — |
| 177 | C4×D4 | — | 6 | 6 | no | — |
| 178 | C4×D4 | — | 6 | 3 | no | — |
| 179 | C4×D4 | — | 6 | 3 | no | — |
| 180 | C4×D4 | — | 6 | 3 | no | — |
| 181 | #117 | — | 3 | 3 | no | — |
| 182 | #117 | — | 3 | 3 | no | — |
| 183 | #117 | — | 3 | 3 | no | — |
| 184 | #117 | — | 6 | 3 | no | — |
| 185 | #117 | — | 6 | 6 | no | — |
| 186 | #117 | — | 6 | 3 | no | — |
| 187 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 188 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 189 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 190 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 191 | C2×C22⋊C4 | — | 6 | 3 | no | — |
| 192 | C2×C42 | — | 3 | 3 | no | — |
| 193 | C2×C42 | — | 6 | 3 | no | — |
| 194 | C2×C42 | — | 6 | 3 | no | — |
| 195 | #107 | — | 3 | 3 | no | — |
| 196 | #107 | — | 3 | 3 | no | — |
| 197 | #106 | — | 3 | 3 | no | — |
| 198 | #106 | — | 3 | 6 | no | — |
| 199 | #106 | — | 3 | 1 | no | — |
| 200 | #103 | — | 3 | 3 | no | — |
| 201 | #103 | — | 3 | 6 | no | — |
| 202 | #103 | — | 3 | 3 | no | — |
| 203 | #103 | — | 3 | 1 | no | — |
| 204 | #103 | — | 3 | 3 | no | — |
| 205 | #102 | — | 3 | 3 | no | — |
| 206 | #102 | — | 3 | 6 | no | — |
| 207 | #102 | — | 3 | 1 | no | — |
| 208 | #102 | — | 3 | 3 | no | — |
| 209 | #102 | — | 3 | 3 | no | — |
| 210 | #97 | — | 3 | 6 | no | — |
| 211 | C4×C8 | — | 3 | 1 | no | — |
| 212 | C4×C8 | — | 3 | 3 | no | — |
| 213 | C4×C8 | — | 3 | 3 | no | — |
| 214 | C4×C8 | — | 3 | 3 | no | — |
| 215 | C22×D3 | — | 4 | 1 | no | — |
| 216 | C3×Q8 | — | 4 | 4 | no | — |
| 217 | C2×C3×C4 | — | 4 | 3 | no | — |
| 218 | C2×C3×C4 | — | 4 | 3 | no | — |
| 219 | C2×C3×C4 | — | 4 | 1 | no | — |
| 220 | C2×Dic3 | — | 4 | 1 | no | — |
| 221 | C2×Dic3 | — | 4 | 3 | no | — |
| 222 | C2×Dic3 | — | 4 | 3 | no | — |
| 223 | C4×D3 | — | 4 | 12 | no | — |
| 224 | C4×D3 | — | 4 | 4 | no | — |
| 225 | C4×D3 | — | 8 | 6 | no | — |
| 226 | Dic6 | — | 4 | 12 | no | — |
| 227 | SL(2,𝔽3) | C23×C4 | 1 | 1 | yes | characteristic |
| 228 | C24 | — | 6 | 1 | no | — |
| 229 | #41 | — | 3 | 4 | no | — |
| 230 | #41 | — | 3 | 4 | no | — |
| 231 | #41 | — | 3 | 6 | no | — |
| 232 | #41 | — | 3 | 12 | no | — |
| 233 | #41 | — | 6 | 6 | no | — |
| 234 | #41 | — | 6 | 24 | no | — |
| 235 | #41 | C2×C4×D3 | 1 | 6 | yes | — |
| 236 | C2×Q8 | — | 3 | 3 | no | — |
| 237 | C2×Q8 | — | 3 | 12 | no | — |
| 238 | C2×Q8 | — | 6 | 6 | no | — |
| 239 | C2×Q8 | — | 6 | 8 | no | — |
| 240 | C2×Q8 | — | 6 | 3 | no | — |
| 241 | C2×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 242 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 243 | C2×D4 | — | 3 | 12 | no | — |
| 244 | C2×D4 | — | 3 | 3 | no | — |
| 245 | C2×D4 | — | 3 | 1 | no | — |
| 246 | C2×D4 | — | 3 | 3 | no | — |
| 247 | C2×D4 | — | 6 | 6 | no | — |
| 248 | C2×D4 | — | 6 | 3 | no | — |
| 249 | C22×C4 | — | 3 | 3 | no | — |
| 250 | C22×C4 | — | 3 | 3 | no | — |
| 251 | C22×C4 | — | 3 | 3 | no | — |
| 252 | C22×C4 | — | 6 | 3 | no | — |
| 253 | C22×C4 | — | 6 | 3 | no | — |
| 254 | C22×C4 | — | 6 | 3 | no | — |
| 255 | C22×C4 | — | 6 | 3 | no | — |
| 256 | C22×C4 | — | 6 | 1 | no | — |
| 257 | C22×C4 | — | 6 | 3 | no | — |
| 258 | C22×C4 | — | 24 | 2 | no | — |
| 259 | Q16 | — | 3 | 6 | no | — |
| 260 | Q16 | — | 3 | 6 | no | — |
| 261 | SD16 | — | 3 | 12 | no | — |
| 262 | SD16 | — | 3 | 24 | no | — |
| 263 | SD16 | — | 3 | 2 | no | — |
| 264 | SD16 | — | 3 | 2 | no | — |
| 265 | D8 | — | 3 | 12 | no | — |
| 266 | M16 | — | 3 | 12 | no | — |
| 267 | M16 | — | 6 | 6 | no | — |
| 268 | C2×C8 | — | 3 | 1 | no | — |
| 269 | C2×C8 | — | 3 | 3 | no | — |
| 270 | C2×C8 | — | 3 | 12 | no | — |
| 271 | C2×C8 | — | 3 | 1 | no | — |
| 272 | C2×C8 | — | 3 | 3 | no | — |
| 273 | C2×C8 | — | 6 | 6 | no | — |
| 274 | C4⋊C4 | — | 3 | 3 | no | — |
| 275 | C4⋊C4 | — | 3 | 1 | no | — |
| 276 | C4⋊C4 | — | 3 | 3 | no | — |
| 277 | C4⋊C4 | — | 3 | 3 | no | — |
| 278 | C4⋊C4 | — | 3 | 1 | no | — |
| 279 | C4⋊C4 | — | 6 | 3 | no | — |
| 280 | C4⋊C4 | — | 6 | 3 | no | — |
| 281 | C4⋊C4 | — | 6 | 3 | no | — |
| 282 | C4⋊C4 | — | 6 | 6 | no | — |
| 283 | C4⋊C4 | C2×S4 | 1 | 3 | yes | — |
| 284 | C22⋊C4 | — | 3 | 6 | no | — |
| 285 | C22⋊C4 | — | 6 | 3 | no | — |
| 286 | C22⋊C4 | — | 6 | 1 | no | — |
| 287 | C22⋊C4 | — | 6 | 3 | no | — |
| 288 | C22⋊C4 | — | 6 | 3 | no | — |
| 289 | C42 | — | 3 | 3 | no | — |
| 290 | C42 | — | 3 | 3 | no | — |
| 291 | C42 | — | 3 | 1 | no | — |
| 292 | C42 | — | 6 | 6 | no | — |
| 293 | C42 | — | 6 | 3 | no | — |
| 294 | C42 | — | 6 | 3 | no | — |
| 295 | C42 | — | 6 | 3 | no | — |
| 296 | C42 | C2×S4 | 1 | 3 | yes | — |
| 297 | C22×C3 | — | 4 | 1 | no | — |
| 298 | C2×D3 | — | 4 | 2 | no | — |
| 299 | C2×D3 | — | 4 | 2 | no | — |
| 300 | C2×D3 | — | 4 | 2 | no | — |
| 301 | C3×C4 | — | 4 | 6 | no | — |
| 302 | C3×C4 | — | 4 | 2 | no | — |
| 303 | C3×C4 | — | 8 | 3 | no | — |
| 304 | Dic3 | — | 4 | 6 | no | — |
| 305 | Dic3 | — | 4 | 2 | no | — |
| 306 | Dic3 | — | 8 | 3 | no | — |
| 307 | C23 | — | 3 | 3 | no | — |
| 308 | C23 | — | 6 | 4 | no | — |
| 309 | C23 | — | 6 | 1 | no | — |
| 310 | C23 | — | 24 | 1 | no | — |
| 311 | C23 | — | 24 | 1 | no | — |
| 312 | Q8 | — | 3 | 1 | no | — |
| 313 | Q8 | — | 3 | 6 | no | — |
| 314 | Q8 | — | 6 | 3 | no | — |
| 315 | Q8 | — | 6 | 12 | no | — |
| 316 | Q8 | C4×S4 | 1 | 4 | yes | — |
| 317 | Q8 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 318 | D4 | — | 3 | 6 | no | — |
| 319 | D4 | — | 3 | 2 | no | — |
| 320 | D4 | — | 3 | 12 | no | — |
| 321 | D4 | — | 6 | 3 | no | — |
| 322 | D4 | — | 6 | 1 | no | — |
| 323 | D4 | — | 6 | 12 | no | — |
| 324 | C2×C4 | — | 3 | 1 | no | — |
| 325 | C2×C4 | — | 3 | 6 | no | — |
| 326 | C2×C4 | — | 3 | 6 | no | — |
| 327 | C2×C4 | — | 3 | 1 | no | — |
| 328 | C2×C4 | — | 3 | 3 | no | — |
| 329 | C2×C4 | — | 6 | 12 | no | — |
| 330 | C2×C4 | — | 6 | 3 | no | — |
| 331 | C2×C4 | — | 6 | 12 | no | — |
| 332 | C2×C4 | — | 6 | 6 | no | — |
| 333 | C2×C4 | — | 6 | 1 | no | — |
| 334 | C2×C4 | — | 6 | 3 | no | — |
| 335 | C2×C4 | — | 12 | 3 | no | — |
| 336 | C2×C4 | — | 12 | 2 | no | — |
| 337 | C2×C4 | — | 24 | 3 | no | — |
| 338 | C2×C4 | — | 24 | 3 | no | — |
| 339 | C2×C4 | — | 24 | 3 | no | — |
| 340 | C2×C4 | C22×S4 | 1 | 3 | yes | — |
| 341 | C2×C4 | C22×S4 | 1 | 3 | yes | — |
| 342 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 343 | C8 | — | 3 | 2 | no | — |
| 344 | C8 | — | 3 | 6 | no | — |
| 345 | C8 | — | 6 | 1 | no | — |
| 346 | C8 | — | 6 | 3 | no | — |
| 347 | C2×C3 | — | 4 | 1 | no | — |
| 348 | C2×C3 | — | 4 | 1 | no | — |
| 349 | C2×C3 | — | 4 | 1 | no | — |
| 350 | D3 | — | 4 | 4 | no | — |
| 351 | C22 | — | 3 | 6 | no | — |
| 352 | C22 | — | 6 | 3 | no | — |
| 353 | C22 | — | 6 | 3 | no | — |
| 354 | C22 | — | 6 | 2 | no | — |
| 355 | C22 | — | 12 | 1 | no | — |
| 356 | C22 | — | 12 | 1 | no | — |
| 357 | C22 | — | 24 | 4 | no | — |
| 358 | C22 | C23×S4 | 1 | 1 | yes | characteristic |
| 359 | C4 | — | 2 | 3 | no | — |
| 360 | C4 | — | 3 | 1 | no | — |
| 361 | C4 | — | 3 | 1 | no | — |
| 362 | C4 | — | 6 | 6 | no | — |
| 363 | C4 | — | 6 | 3 | no | — |
| 364 | C4 | — | 6 | 1 | no | — |
| 365 | C4 | — | 12 | 1 | no | — |
| 366 | C4 | — | 12 | 3 | no | — |
| 367 | C4 | C2×C4×S4 | 1 | 6 | yes | — |
| 368 | C4 | #5924 | 1 | 2 | yes | direct product factor |
| 369 | C3 | — | 4 | 1 | no | Sylow |
| 370 | C2 | — | 6 | 6 | no | — |
| 371 | C2 | — | 12 | 2 | no | — |
| 372 | C2 | C22×C4×S4 | 1 | 1 | yes | characteristic |
| 373 | C2 | C2×#5924 | 1 | 1 | yes | characteristic |
| 374 | C2 | #87497 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#994 | C2 | semidirect |
| 3. #85528 | C2 | semidirect |
| 4. #85364 | C2 | semidirect |
| 5. #85360 | C2 | semidirect |
| 6. C4×#985 | C2 | semidirect |
| 7. C4×#984 | C2 | semidirect |
| 10. #5924 | C4 | direct (N × H) |
| 18. C4×GL(2,𝔽3) | C22 | semidirect |
| 19. C4×GL(2,𝔽3) | C22 | semidirect |
| 20. #5388 | C22 | semidirect |
| 21. C4×#226 | C22 | semidirect |
| 22. C4×#226 | C22 | semidirect |
| 25. C4×H(5,𝔽2) | D3 | semidirect |
| 39. #994 | C2×C4 | semidirect |
| 41. #985 | C2×C4 | semidirect |
| 42. #984 | C2×C4 | semidirect |
| 119. GL(2,𝔽3) | C22×C4 | semidirect |
| 120. #226 | C22×C4 | semidirect |
| 131. H(5,𝔽2) | C4×D3 | semidirect |
| 368. C4 | #5924 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5924 | 2 |
| C4×#994 | 2 |
| #85528 | 2 |
| #85364 | 2 |
| #85360 | 2 |
| C4×#985 | 2 |
| C4×#984 | 2 |
| C4×#577 | 3 |
| C4×D3×Q8 | 4 |