Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
212 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 95 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×D479 |
| commutator, socle, cosocle | C22×C479 | C24 |
| Fitting | #126×C479 | C2 |
| prime radical | C2×C22⋊D479 | C22 |
| hypercenter | #126 | D479 |
| hypocenter | C479 | #556 |
| LCS | G ▷ C22×C479 ▷ C479 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #29506381 | C2 | semidirect |
| 2. #29506377 | C2 | semidirect |
| 3. #29506377 | C2 | semidirect |
| 4. #29506375 | C2 | semidirect |
| 7. #29506360 | C2 | semidirect |
| 8. #29506359 | C2 | semidirect |
| 9. C4×Dic958 | C2 | semidirect |
| 10. #29506347 | C2 | semidirect |
| 11. #29506347 | C2 | semidirect |
| 13. #29506339 | C2 | semidirect |
| 14. #29506338 | C2 | semidirect |
| 15. #126×C479 | C2 | semidirect |
| 97. C479 | #556 | semidirect |
| 103. #126 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506381 | 2 |
| #29506377 | 2 |
| #29506375 | 2 |
| #29506368 | 2 |
| #29506360 | 2 |
| #29506359 | 2 |
| C4×Dic958 | 2 |
| #29506347 | 2 |
| (C22⋊D479)⋊C4 | 2 |
| #29506339 | 2 |
| #29506338 | 2 |
| #126×C479 | 2 |
| #556 | 479 |