Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D233 |
| commutator, socle, cosocle | C22×C233 | C24 |
| Fitting | #123×C233 | C2 |
| hypercenter | #123 | D233 |
| hypocenter | C233 | #538 |
| LCS | G ▷ C22×C233 ▷ C233 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21418530 | C2 | semidirect |
| 2. #21418528 | C2 | semidirect |
| 3. #21418521 | C2 | semidirect |
| 4. #21418521 | C2 | semidirect |
| 5. #21418520 | C2 | semidirect |
| 6. #21418515 | C2 | semidirect |
| 7. #21418509 | C2 | semidirect |
| 8. #21418508 | C2 | semidirect |
| 9. #21418506 | C2 | semidirect |
| 10. #21418505 | C2 | semidirect |
| 11. #21418503 | C2 | semidirect |
| 12. #21418497 | C2 | semidirect |
| 13. C4×C22⋊D233 | C2 | semidirect |
| 14. C22⋊C4×D233 | C2 | semidirect |
| 15. #123×C233 | C2 | semidirect |
| 17. C2×Dic466 | C22 | semidirect |
| 23. C2×C22⋊D233 | C22 | semidirect |
| 26. C2×C4×D233 | C22 | semidirect |
| 27. C4⋊Dic233 | C22 | semidirect |
| 28. C4⋊Dic233 | C22 | semidirect |
| 29. #16836573 | C22 | semidirect |
| 30. #16836573 | C22 | semidirect |
| 33. C22⋊Dic233 | C22 | semidirect |
| 40. #16836571 | C22 | semidirect |
| 41. #16836571 | C22 | semidirect |
| 42. C4×Dic233 | C22 | semidirect |
| 43. C4×Dic233 | C22 | semidirect |
| 45. C22×C4×C233 | C22 | semidirect |
| 46. C4⋊C4×C233 | C22 | semidirect |
| 47. C4⋊C4×C233 | C22 | semidirect |
| 50. C22⋊C4×C233 | C22 | semidirect |
| 116. C233 | #538 | semidirect |
| 123. #123 | D233 | semidirect |
| 145. C22×C4 | C2×D233 | semidirect |
| 150. C4⋊C4 | C2×D233 | semidirect |
| 151. C4⋊C4 | C2×D233 | semidirect |
| 165. C22⋊C4 | C2×D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21418530 | 2 |
| #21418528 | 2 |
| #21418521 | 2 |
| #21418520 | 2 |
| #21418515 | 2 |
| #21418509 | 2 |
| #21418508 | 2 |
| #21418506 | 2 |
| #21418505 | 2 |
| #21418503 | 2 |
| #21418497 | 2 |
| C4×C22⋊D233 | 2 |
| C22⋊C4×D233 | 2 |
| #123×C233 | 2 |
| #538 | 233 |