Finite Group DatabasebetaFinite Group DatabasebetaOrder 36928.
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×D577 |
| commutator, socle, cosocle | C22×C577 | C24 |
| Fitting | #123×C577 | C2 |
| prime radical | #32914636 | C2 |
| hypercenter | #123 | D577 |
| hypocenter | C577 | #529 |
| LCS | G ▷ C22×C577 ▷ C577 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #32914659 | C2 | semidirect |
| 2. #32914657 | C2 | semidirect |
| 3. #32914654 | C2 | semidirect |
| 4. #32914650 | C2 | semidirect |
| 5. #32914647 | C2 | semidirect |
| 6. #32914641 | C2 | semidirect |
| 8. #32914629 | C2 | semidirect |
| 9. D4×Dic577 | C2 | semidirect |
| 10. #32914624 | C2 | semidirect |
| 11. #32914624 | C2 | semidirect |
| 12. #32914622 | C2 | semidirect |
| 13. #32914620 | C2 | semidirect |
| 14. C2×C4×Dic577 | C2 | semidirect |
| 15. #123×C577 | C2 | semidirect |
| 103. C577 | #529 | semidirect |
| 110. #123 | D577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #32914659 | 2 |
| #32914657 | 2 |
| #32914654 | 2 |
| #32914650 | 2 |
| #32914647 | 2 |
| #32914641 | 2 |
| #32914636 | 2 |
| #32914629 | 2 |
| D4×Dic577 | 2 |
| #32914624 | 2 |
| #32914622 | 2 |
| #32914620 | 2 |
| C2×C4×Dic577 | 2 |
| #123×C577 | 2 |
| #529 | 577 |