Finite Group DatabasebetaFinite Group DatabasebetaOrder 36928.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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 | C2×#22604417 | C2 |
| hypercenter | #123 | D577 |
| hypocenter | C577 | #536 |
| LCS | G ▷ C22×C577 ▷ C577 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic1154 | C2 | semidirect |
| 3. #32914663 | C2 | semidirect |
| 4. #32914650 | C2 | semidirect |
| 5. #32914648 | C2 | semidirect |
| 6. #32914647 | C2 | semidirect |
| 7. #32914645 | C2 | semidirect |
| 8. #32914642 | C2 | semidirect |
| 9. #32914641 | C2 | semidirect |
| 10. #32914620 | C2 | semidirect |
| 11. #123×C577 | C2 | semidirect |
| 79. C577 | #536 | semidirect |
| 88. #123 | D577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22604417 | 2 |
| C22×Dic1154 | 2 |
| #32914663 | 2 |
| #32914650 | 2 |
| #32914648 | 2 |
| #32914647 | 2 |
| #32914645 | 2 |
| #32914642 | 2 |
| #32914641 | 2 |
| #32914620 | 2 |
| #123×C577 | 2 |
| #536 | 577 |