Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
234 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 234 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×D479 |
| commutator, socle, cosocle | C22×C479 | C24 |
| Fitting | #126×C479 | C2 |
| prime radical | #29506355 | C2 |
| hypercenter | #126 | D479 |
| hypocenter | C479 | #529 |
| 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. #29506376 | C2 | semidirect |
| 2. #29506372 | C2 | semidirect |
| 3. #29506368 | C2 | semidirect |
| 4. #29506367 | C2 | semidirect |
| 5. #29506364 | C2 | semidirect |
| 6. #29506360 | C2 | semidirect |
| 8. #29506347 | C2 | semidirect |
| 9. #29506344 | C2 | semidirect |
| 10. (C22⋊D479)⋊C4 | C2 | semidirect |
| 11. (C22⋊D479)⋊C4 | C2 | semidirect |
| 12. #29506340 | C2 | semidirect |
| 13. #29506338 | C2 | semidirect |
| 14. C42×D479 | C2 | semidirect |
| 15. #126×C479 | C2 | semidirect |
| 103. C479 | #529 | semidirect |
| 106. #126 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506376 | 2 |
| #29506372 | 2 |
| #29506368 | 2 |
| #29506367 | 2 |
| #29506364 | 2 |
| #29506360 | 2 |
| #29506355 | 2 |
| #29506347 | 2 |
| #29506344 | 2 |
| (C22⋊D479)⋊C4 | 2 |
| #29506340 | 2 |
| #29506338 | 2 |
| C42×D479 | 2 |
| #126×C479 | 2 |
| #529 | 479 |