Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26042015 | C2 | semidirect |
| 2. #26041986 | C2 | semidirect |
| 3. #26041632 | C2 | semidirect |
| 4. #26041625 | C2 | semidirect |
| 5. #26041577 | C2 | semidirect |
| 6. #26041575 | C2 | semidirect |
| 7. #26041492 | C2 | semidirect |
| 8. #26041403 | C2 | semidirect |
| 9. C4×#15668437 | C2 | semidirect |
| 10. D8×Dic181 | C2 | semidirect |
| 122. C181 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042015 | 2 |
| #26041986 | 2 |
| #26041632 | 2 |
| #26041625 | 2 |
| #26041577 | 2 |
| #26041575 | 2 |
| #26041492 | 2 |
| #26041403 | 2 |
| C4×#15668437 | 2 |
| D8×Dic181 | 2 |
| #459×C181 | 2 |
| #3361 | 181 |