Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 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. #26041831 | C2 | semidirect |
| 3. #26041672 | C2 | semidirect |
| 4. #26041640 | C2 | semidirect |
| 5. #26041504 | C2 | semidirect |
| 6. #26041503 | C2 | semidirect |
| 7. #26041435 | C2 | semidirect |
| 10. #26041333 | C2 | semidirect |
| 11. #451×C181 | C2 | semidirect |
| 13. C2×#15668439 | C22 | semidirect |
| 16. #19153815 | C22 | semidirect |
| 17. #19153814 | C22 | semidirect |
| 25. Q8×Dic181 | C22 | semidirect |
| 27. #19153781 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153740 | C22 | semidirect |
| 37. #19153726 | C22 | semidirect |
| 39. C2×Q16×C181 | C22 | semidirect |
| 41. #103×C181 | C22 | semidirect |
| 139. C181 | #3215 | semidirect |
| 148. #451 | D181 | semidirect |
| 155. C2×Q16 | C2×D181 | semidirect |
| 177. #103 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041831 | 2 |
| C2×#19153805 | 2 |
| #26041672 | 2 |
| #26041640 | 2 |
| #26041504 | 2 |
| #26041503 | 2 |
| #26041435 | 2 |
| #26041432 | 2 |
| #26041429 | 2 |
| #26041333 | 2 |
| #451×C181 | 2 |
| #3215 | 181 |