Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 1. #26042001 | C2 | semidirect |
| 2. #26041672 | C2 | semidirect |
| 4. #26041501 | C2 | semidirect |
| 6. #26041488 | C2 | semidirect |
| 7. #26041409 | C2 | semidirect |
| 8. #26041378 | C2 | semidirect |
| 9. C4×Q16×C181 | C2 | semidirect |
| 102. C181 | #3402 | semidirect |
| 112. C4×Q16 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042001 | 2 |
| #26041672 | 2 |
| #26041663 | 2 |
| #26041501 | 2 |
| #26041497 | 2 |
| #26041488 | 2 |
| #26041409 | 2 |
| #26041378 | 2 |
| C4×Q16×C181 | 2 |
| #3402 | 181 |