Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26041834 | C2 | semidirect |
| 3. #26041616 | C2 | semidirect |
| 4. #26041556 | C2 | semidirect |
| 5. #26041485 | C2 | semidirect |
| 6. #26041484 | C2 | semidirect |
| 8. #26041378 | C2 | semidirect |
| 9. #26041376 | C2 | semidirect |
| 10. #26041335 | C2 | semidirect |
| 11. #474×C181 | C2 | semidirect |
| 16. #19153816 | C22 | semidirect |
| 21. #19153781 | C22 | semidirect |
| 31. #19153749 | C22 | semidirect |
| 32. C4⋊#13089678 | C22 | semidirect |
| 33. #19153741 | C22 | semidirect |
| 34. #19153739 | C22 | semidirect |
| 37. #19153726 | C22 | semidirect |
| 38. C4⋊Q8×C181 | C22 | semidirect |
| 40. #107×C181 | C22 | semidirect |
| 41. C4⋊C8×C181 | C22 | semidirect |
| 146. C181 | #3110 | semidirect |
| 152. #474 | D181 | semidirect |
| 164. C4⋊Q8 | C2×D181 | semidirect |
| 181. #107 | C2×D181 | semidirect |
| 183. C4⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| C4×D4×D181 | 2 |
| #26041616 | 2 |
| #26041556 | 2 |
| #26041485 | 2 |
| #26041484 | 2 |
| #26041431 | 2 |
| #26041378 | 2 |
| #26041376 | 2 |
| #26041335 | 2 |
| #474×C181 | 2 |
| #3110 | 181 |