Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 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. #26042002 | C2 | semidirect |
| 3. #26041659 | C2 | semidirect |
| 4. #26041502 | C2 | semidirect |
| 5. #26041485 | C2 | semidirect |
| 6. C4×Dic724 | C2 | semidirect |
| 8. C8×Q8×C181 | C2 | semidirect |
| 84. C181 | #3393 | semidirect |
| 91. C8×Q8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042002 | 2 |
| #26041663 | 2 |
| #26041659 | 2 |
| #26041502 | 2 |
| #26041485 | 2 |
| C4×Dic724 | 2 |
| C4×D1448 | 2 |
| C8×Q8×C181 | 2 |
| #3393 | 181 |