Finite Group DatabasebetaFinite Group DatabasebetaOrder 29632.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 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 | #120×C463 | C2 |
| hypercenter | #120 | D463 |
| hypocenter | C463 | #560 |
| LCS | G ▷ C22×C463 ▷ C463 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28414654 | C2 | semidirect |
| 2. #28414651 | C2 | semidirect |
| 3. #28414640 | C2 | semidirect |
| 4. #28414639 | C2 | semidirect |
| 5. #28414631 | C2 | semidirect |
| 6. #28414630 | C2 | semidirect |
| 7. #28414629 | C2 | semidirect |
| 8. #28414627 | C2 | semidirect |
| 9. #120×C463 | C2 | semidirect |
| 10. C2×D1852 | C22 | semidirect |
| 14. C2×C22⋊D463 | C22 | semidirect |
| 15. C22×Dic463 | C22 | semidirect |
| 16. C2×C4×D463 | C22 | semidirect |
| 17. C4⋊Dic463 | C22 | semidirect |
| 18. Dic463⋊C4 | C22 | semidirect |
| 19. Dic463⋊C4 | C22 | semidirect |
| 23. C22⋊Dic463 | C22 | semidirect |
| 24. (C2×D463)⋊C4 | C22 | semidirect |
| 25. C4×Dic463 | C22 | semidirect |
| 74. C463 | #560 | semidirect |
| 84. #120 | D463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28414654 | 2 |
| #28414651 | 2 |
| #28414640 | 2 |
| #28414639 | 2 |
| #28414631 | 2 |
| #28414630 | 2 |
| #28414629 | 2 |
| #28414627 | 2 |
| #120×C463 | 2 |
| #560 | 463 |