Finite Group DatabasebetaFinite Group DatabasebetaOrder 33472.
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×D523 |
| commutator, socle, cosocle | C22×C523 | C24 |
| Fitting | #126×C523 | C2 |
| hypercenter | #126 | D523 |
| hypocenter | C523 | #538 |
| LCS | G ▷ C22×C523 ▷ C523 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30660368 | C2 | semidirect |
| 2. #30660361 | C2 | semidirect |
| 3. #30660359 | C2 | semidirect |
| 4. #30660358 | C2 | semidirect |
| 5. #30660355 | C2 | semidirect |
| 6. #30660351 | C2 | semidirect |
| 7. #30660348 | C2 | semidirect |
| 8. #30660348 | C2 | semidirect |
| 9. #30660346 | C2 | semidirect |
| 10. #30660343 | C2 | semidirect |
| 11. #30660343 | C2 | semidirect |
| 12. C4×D2092 | C2 | semidirect |
| 13. #30660335 | C2 | semidirect |
| 14. C22⋊C4×D523 | C2 | semidirect |
| 15. #126×C523 | C2 | semidirect |
| 17. C2×Dic1046 | C22 | semidirect |
| 22. C2×D2092 | C22 | semidirect |
| 27. C2×C4×D523 | C22 | semidirect |
| 28. C2×C4×D523 | C22 | semidirect |
| 29. C4⋊Dic523 | C22 | semidirect |
| 30. Dic523⋊C4 | C22 | semidirect |
| 31. Dic523⋊C4 | C22 | semidirect |
| 39. (C2×D523)⋊C4 | C22 | semidirect |
| 40. (C2×D523)⋊C4 | C22 | semidirect |
| 41. (C2×D523)⋊C4 | C22 | semidirect |
| 42. (C2×D523)⋊C4 | C22 | semidirect |
| 43. C4×Dic523 | C22 | semidirect |
| 44. C4⋊C4×C523 | C22 | semidirect |
| 45. C4⋊C4×C523 | C22 | semidirect |
| 46. C4⋊C4×C523 | C22 | semidirect |
| 50. C42×C523 | C22 | semidirect |
| 116. C523 | #538 | semidirect |
| 119. #126 | D523 | semidirect |
| 149. C4⋊C4 | C2×D523 | semidirect |
| 150. C4⋊C4 | C2×D523 | semidirect |
| 151. C4⋊C4 | C2×D523 | semidirect |
| 167. C42 | C2×D523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30660368 | 2 |
| #30660361 | 2 |
| #30660359 | 2 |
| #30660358 | 2 |
| #30660355 | 2 |
| #30660351 | 2 |
| #30660348 | 2 |
| #30660346 | 2 |
| #30660343 | 2 |
| C4×D2092 | 2 |
| #30660335 | 2 |
| C22⋊C4×D523 | 2 |
| #126×C523 | 2 |
| #538 | 523 |