Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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 | #123×C479 | C2 |
| prime radical | #29506354 | C2 |
| hypercenter | #123 | D479 |
| hypocenter | C479 | #529 |
| LCS | G ▷ C22×C479 ▷ C479 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #29506377 | C2 | semidirect |
| 2. #29506375 | C2 | semidirect |
| 3. #29506372 | C2 | semidirect |
| 4. #29506368 | C2 | semidirect |
| 5. #29506365 | C2 | semidirect |
| 6. #29506359 | C2 | semidirect |
| 8. #29506347 | C2 | semidirect |
| 9. D4×Dic479 | C2 | semidirect |
| 10. (C22⋊D479)⋊C4 | C2 | semidirect |
| 11. (C22⋊D479)⋊C4 | C2 | semidirect |
| 12. #29506340 | C2 | semidirect |
| 13. #29506338 | C2 | semidirect |
| 14. C2×C4×Dic479 | C2 | semidirect |
| 15. #123×C479 | C2 | semidirect |
| 103. C479 | #529 | semidirect |
| 110. #123 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506377 | 2 |
| #29506375 | 2 |
| #29506372 | 2 |
| #29506368 | 2 |
| #29506365 | 2 |
| #29506359 | 2 |
| #29506354 | 2 |
| #29506347 | 2 |
| D4×Dic479 | 2 |
| (C22⋊D479)⋊C4 | 2 |
| #29506340 | 2 |
| #29506338 | 2 |
| C2×C4×Dic479 | 2 |
| #123×C479 | 2 |
| #529 | 479 |