Finite Group DatabasebetaFinite Group DatabasebetaOrder 36928.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 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 |
| prime radical | #32914635 | C2 |
| hypercenter | C4×D4 | D577 |
| hypocenter | C577 | #542 |
| 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. #32914663 | C2 | semidirect |
| 2. #32914657 | C2 | semidirect |
| 3. #32914651 | C2 | semidirect |
| 4. #32914650 | C2 | semidirect |
| 5. #32914647 | C2 | semidirect |
| 6. #32914644 | C2 | semidirect |
| 7. #32914643 | C2 | semidirect |
| 9. C4×Dic1154 | C2 | semidirect |
| 10. #32914621 | C2 | semidirect |
| 11. C4×D4×C577 | C2 | semidirect |
| 73. C577 | #542 | semidirect |
| 84. C4×D4 | D577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #32914663 | 2 |
| #32914657 | 2 |
| #32914651 | 2 |
| #32914650 | 2 |
| #32914647 | 2 |
| #32914644 | 2 |
| #32914643 | 2 |
| #32914635 | 2 |
| C4×Dic1154 | 2 |
| #32914621 | 2 |
| C4×D4×C577 | 2 |
| #542 | 577 |