Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
3262 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 3262 conjugacy classes of subgroups — too many to draw. Only its 987 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#17986378 | C2 | direct (N × H) |
| 13. #17986378 | C22 | direct (N × H) |
| 60. C22×C4×C71 | Q16 | semidirect |
| 76. C2×C4×C71 | C2×Q16 | semidirect |
| 86. C22×C71 | #494 | semidirect |
| 92. C4×C71 | C22×Q16 | semidirect |
| 96. C2×C71 | C2×#494 | semidirect |
| 104. C71 | C22×#494 | semidirect |
| 155. C22×C4 | #11765855 | semidirect |
| 179. C2×C4 | C2×#11765855 | semidirect |
| 185. C22 | #17986378 | direct (N × H) |
| 192. C4 | C22×#11765855 | semidirect |
| 194. C2 | C2×#17986378 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11765855 | 2 |
| C22×#14556128 | 2 |
| C2×#17986378 | 2 |
| C22×C4×C71⋊C8 | 2 |
| C22×C4⋊Q8×C71 | 2 |
| C22×#494 | 71 |