Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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 | #546 |
| 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. C2×#16836594 | C2 | semidirect |
| 2. C2×D4×D233 | C2 | semidirect |
| 3. #21418521 | C2 | semidirect |
| 4. #21418520 | C2 | semidirect |
| 5. #21418513 | C2 | semidirect |
| 6. #21418510 | C2 | semidirect |
| 7. #21418508 | C2 | semidirect |
| 8. #21418507 | C2 | semidirect |
| 9. #21418505 | C2 | semidirect |
| 10. #21418505 | C2 | semidirect |
| 11. #21418497 | C2 | semidirect |
| 12. #21418495 | C2 | semidirect |
| 13. C2×#16836571 | C2 | semidirect |
| 14. C22⋊C4×D233 | C2 | semidirect |
| 15. #123×C233 | C2 | semidirect |
| 19. C2×Dic466 | C22 | semidirect |
| 22. C2×D932 | C22 | semidirect |
| 23. C2×D932 | C22 | semidirect |
| 26. C2×C22⋊D233 | C22 | semidirect |
| 27. C2×C22⋊D233 | C22 | semidirect |
| 29. C22×Dic233 | C22 | semidirect |
| 31. C2×C4×D233 | C22 | semidirect |
| 32. C2×C4×D233 | C22 | semidirect |
| 33. C2×C4×D233 | C22 | semidirect |
| 34. #16836573 | C22 | semidirect |
| 35. #16836573 | C22 | semidirect |
| 36. C22⋊Dic233 | C22 | semidirect |
| 40. #16836571 | C22 | semidirect |
| 41. #16836571 | C22 | semidirect |
| 42. #16836571 | C22 | semidirect |
| 43. #16836571 | C22 | semidirect |
| 44. #16836571 | C22 | semidirect |
| 45. C4×Dic233 | C22 | semidirect |
| 47. C22×C4×C233 | C22 | semidirect |
| 48. C4⋊C4×C233 | C22 | semidirect |
| 49. C4⋊C4×C233 | C22 | semidirect |
| 50. C22⋊C4×C233 | C22 | semidirect |
| 51. C22⋊C4×C233 | C22 | semidirect |
| 52. C22⋊C4×C233 | C22 | semidirect |
| 71. C22⋊D233 | D4 | semidirect |
| 110. C2×D233 | #41 | semidirect |
| 129. C233 | #546 | semidirect |
| 135. #123 | D233 | semidirect |
| 165. C22×C4 | C2×D233 | semidirect |
| 168. C4⋊C4 | C2×D233 | semidirect |
| 169. C4⋊C4 | C2×D233 | semidirect |
| 179. C22⋊C4 | C2×D233 | semidirect |
| 180. C22⋊C4 | C2×D233 | semidirect |
| 181. C22⋊C4 | C2×D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16836594 | 2 |
| C2×D4×D233 | 2 |
| #21418521 | 2 |
| #21418520 | 2 |
| #21418513 | 2 |
| #21418510 | 2 |
| #21418508 | 2 |
| #21418507 | 2 |
| #21418505 | 2 |
| #21418497 | 2 |
| #21418495 | 2 |
| C2×#16836571 | 2 |
| C22⋊C4×D233 | 2 |
| #123×C233 | 2 |
| #546 | 233 |