Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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 | #117×C233 | C2 |
| prime radical | #21418505 | C2 |
| hypercenter | #117 | D233 |
| hypocenter | C233 | #551 |
| LCS | G ▷ C22×C233 ▷ C233 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21418530 | C2 | semidirect |
| 2. #21418529 | C2 | semidirect |
| 3. #21418523 | C2 | semidirect |
| 4. #21418520 | C2 | semidirect |
| 5. #21418520 | C2 | semidirect |
| 6. #21418518 | C2 | semidirect |
| 7. #21418513 | C2 | semidirect |
| 8. #21418512 | C2 | semidirect |
| 10. C4×D932 | C2 | semidirect |
| 11. #21418495 | C2 | semidirect |
| 12. #21418492 | C2 | semidirect |
| 13. C2×#16836571 | C2 | semidirect |
| 14. C22⋊C4×D233 | C2 | semidirect |
| 15. #117×C233 | C2 | semidirect |
| 17. C2×Dic466 | C22 | semidirect |
| 24. C2×C4×D233 | C22 | semidirect |
| 25. C4⋊Dic233 | C22 | semidirect |
| 26. #16836573 | C22 | semidirect |
| 27. #16836573 | C22 | semidirect |
| 28. #16836573 | C22 | semidirect |
| 29. #16836573 | C22 | semidirect |
| 30. #16836573 | C22 | semidirect |
| 40. #16836571 | C22 | semidirect |
| 41. #16836571 | C22 | semidirect |
| 42. #16836571 | C22 | semidirect |
| 43. C4×Dic233 | C22 | semidirect |
| 45. C4⋊C4×C233 | C22 | semidirect |
| 46. C4⋊C4×C233 | C22 | semidirect |
| 49. C42×C233 | C22 | semidirect |
| 50. C42×C233 | C22 | semidirect |
| 110. C233 | #551 | semidirect |
| 124. #117 | D233 | semidirect |
| 143. C4⋊C4 | C2×D233 | semidirect |
| 144. C4⋊C4 | C2×D233 | semidirect |
| 160. C42 | C2×D233 | semidirect |
| 161. C42 | C2×D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21418530 | 2 |
| #21418529 | 2 |
| #21418523 | 2 |
| #21418520 | 2 |
| #21418518 | 2 |
| #21418513 | 2 |
| #21418512 | 2 |
| #21418505 | 2 |
| C4×D932 | 2 |
| #21418495 | 2 |
| #21418492 | 2 |
| C2×#16836571 | 2 |
| C22⋊C4×D233 | 2 |
| #117×C233 | 2 |
| #551 | 233 |