Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#19153840 | C2 | semidirect |
| 2. #26041924 | C2 | semidirect |
| 3. #26041663 | C2 | semidirect |
| 4. #26041526 | C2 | semidirect |
| 5. #26041494 | C2 | semidirect |
| 6. #26041442 | C2 | semidirect |
| 7. #26041414 | C2 | semidirect |
| 8. #26041358 | C2 | semidirect |
| 9. C4×D8×C181 | C2 | semidirect |
| 11. C2×D4×D181 | C22 | semidirect |
| 13. C2×Dic724 | C22 | semidirect |
| 14. C2×#15668438 | C22 | semidirect |
| 15. C2×#15668437 | C22 | semidirect |
| 18. C2×#15668432 | C22 | semidirect |
| 19. #19153804 | C22 | semidirect |
| 21. #19153796 | C22 | semidirect |
| 27. C4⋊#13089678 | C22 | semidirect |
| 28. #19153739 | C22 | semidirect |
| 29. #19153736 | C22 | semidirect |
| 30. #19153728 | C22 | semidirect |
| 32. C4×D4×C181 | C22 | semidirect |
| 33. #107×C181 | C22 | semidirect |
| 34. #102×C181 | C22 | semidirect |
| 35. C4×C8×C181 | C22 | semidirect |
| 65. D8×C181 | D4 | semidirect |
| 124. C181 | #3273 | semidirect |
| 133. C4×D8 | D181 | semidirect |
| 152. C4×D4 | C2×D181 | semidirect |
| 154. #107 | C2×D181 | semidirect |
| 158. #102 | C2×D181 | semidirect |
| 160. C4×C8 | C2×D181 | semidirect |
| 181. D8 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153840 | 2 |
| #26041924 | 2 |
| #26041663 | 2 |
| #26041526 | 2 |
| #26041494 | 2 |
| #26041442 | 2 |
| #26041414 | 2 |
| #26041358 | 2 |
| C4×D8×C181 | 2 |
| #3273 | 181 |