Finite Group DatabasebetaFinite Group DatabasebetaOrder 36928.
240 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 240 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×D577 |
| commutator, socle, cosocle | C22×C577 | C24 |
| Fitting | C4×D4×C577 | C2 |
| hypercenter | C4×D4 | D577 |
| hypocenter | C577 | #540 |
| LCS | G ▷ C22×C577 ▷ C577 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #32914660 | C2 | semidirect |
| 2. #32914655 | C2 | semidirect |
| 3. #32914647 | C2 | semidirect |
| 4. #32914646 | C2 | semidirect |
| 5. #32914639 | C2 | semidirect |
| 6. #32914638 | C2 | semidirect |
| 7. #32914637 | C2 | semidirect |
| 8. #32914635 | C2 | semidirect |
| 9. C4×D2308 | C2 | semidirect |
| 10. #32914621 | C2 | semidirect |
| 11. C4×D4×C577 | C2 | semidirect |
| 79. C577 | #540 | semidirect |
| 90. C4×D4 | D577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #32914660 | 2 |
| #32914655 | 2 |
| #32914647 | 2 |
| #32914646 | 2 |
| #32914639 | 2 |
| #32914638 | 2 |
| #32914637 | 2 |
| #32914635 | 2 |
| C4×D2308 | 2 |
| #32914621 | 2 |
| C4×D4×C577 | 2 |
| #540 | 577 |