Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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. #26041990 | C2 | semidirect |
| 3. #26041627 | C2 | semidirect |
| 4. #26041599 | C2 | semidirect |
| 5. #26041509 | C2 | semidirect |
| 6. #26041480 | C2 | semidirect |
| 7. #26041431 | C2 | semidirect |
| 8. C4×#15668437 | C2 | semidirect |
| 9. #26041344 | C2 | semidirect |
| 10. #102×D181 | C2 | semidirect |
| 11. #476×C181 | C2 | semidirect |
| 14. C2×#15668438 | C22 | semidirect |
| 16. C2×C8×D181 | C22 | semidirect |
| 19. #19153796 | C22 | semidirect |
| 24. C4×Dic362 | C22 | semidirect |
| 27. C4⋊C4×D181 | C22 | semidirect |
| 28. #19153747 | C22 | semidirect |
| 29. #19153739 | C22 | semidirect |
| 30. #19153738 | C22 | semidirect |
| 32. #19153736 | C22 | semidirect |
| 33. #19153736 | C22 | semidirect |
| 34. #19153728 | C22 | semidirect |
| 35. C4×#13089678 | C22 | semidirect |
| 36. C4⋊Q8×C181 | C22 | semidirect |
| 38. #106×C181 | C22 | semidirect |
| 39. C4⋊C8×C181 | C22 | semidirect |
| 89. D724 | SD16 | semidirect |
| 136. C181 | #3295 | semidirect |
| 142. #476 | D181 | semidirect |
| 154. C4⋊Q8 | C2×D181 | semidirect |
| 168. #106 | C2×D181 | semidirect |
| 169. C4⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041990 | 2 |
| D4×D724 | 2 |
| #26041627 | 2 |
| #26041599 | 2 |
| #26041509 | 2 |
| #26041480 | 2 |
| #26041431 | 2 |
| C4×#15668437 | 2 |
| #26041344 | 2 |
| #102×D181 | 2 |
| #476×C181 | 2 |
| #3295 | 181 |