Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26042008 | C2 | semidirect |
| 4. #26041659 | C2 | semidirect |
| 6. #26041490 | C2 | semidirect |
| 7. #26041490 | C2 | semidirect |
| 9. #26041387 | C2 | semidirect |
| 11. #446×C181 | C2 | semidirect |
| 119. C181 | #3398 | semidirect |
| 129. #446 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042008 | 2 |
| #26042002 | 2 |
| #26041673 | 2 |
| #26041659 | 2 |
| #26041502 | 2 |
| #26041490 | 2 |
| #26041485 | 2 |
| #26041387 | 2 |
| C4×#15668438 | 2 |
| #446×C181 | 2 |
| #3398 | 181 |