Finite Group DatabasebetaFinite Group DatabasebetaOrder 29632.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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×D463 |
| commutator, socle, cosocle | C22×C463 | C24 |
| Fitting | #126×C463 | C2 |
| prime radical | C2×C22⋊D463 | C22 |
| hypercenter | #126 | D463 |
| hypocenter | C463 | #563 |
| LCS | G ▷ C22×C463 ▷ C463 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28414658 | C2 | semidirect |
| 2. #28414657 | C2 | semidirect |
| 3. #28414653 | C2 | semidirect |
| 4. #28414652 | C2 | semidirect |
| 5. #28414651 | C2 | semidirect |
| 6. #28414649 | C2 | semidirect |
| 7. #28414648 | C2 | semidirect |
| 11. #28414638 | C2 | semidirect |
| 12. #28414636 | C2 | semidirect |
| 13. #28414635 | C2 | semidirect |
| 14. #28414635 | C2 | semidirect |
| 15. #126×C463 | C2 | semidirect |
| 97. C463 | #563 | semidirect |
| 104. #126 | D463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28414658 | 2 |
| #28414657 | 2 |
| #28414653 | 2 |
| #28414652 | 2 |
| #28414651 | 2 |
| #28414649 | 2 |
| #28414648 | 2 |
| #28414644 | 2 |
| #28414642 | 2 |
| #28414640 | 2 |
| #28414638 | 2 |
| #28414636 | 2 |
| #28414635 | 2 |
| #126×C463 | 2 |
| #563 | 463 |