Finite Group DatabasebetaFinite Group DatabasebetaOrder 37568.
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×D587 |
| commutator, socle, cosocle | C22×C587 | C24 |
| Fitting | #123×C587 | C2 |
| prime radical | #34037593 | C2 |
| hypercenter | #123 | D587 |
| hypocenter | C587 | #529 |
| LCS | G ▷ C22×C587 ▷ C587 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #34037616 | C2 | semidirect |
| 2. #34037614 | C2 | semidirect |
| 3. #34037611 | C2 | semidirect |
| 4. #34037607 | C2 | semidirect |
| 5. #34037604 | C2 | semidirect |
| 6. #34037598 | C2 | semidirect |
| 8. #34037586 | C2 | semidirect |
| 9. D4×Dic587 | C2 | semidirect |
| 10. (C22⋊D587)⋊C4 | C2 | semidirect |
| 11. (C22⋊D587)⋊C4 | C2 | semidirect |
| 12. #34037579 | C2 | semidirect |
| 13. #34037577 | C2 | semidirect |
| 14. C2×C4×Dic587 | C2 | semidirect |
| 15. #123×C587 | C2 | semidirect |
| 103. C587 | #529 | semidirect |
| 110. #123 | D587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34037616 | 2 |
| #34037614 | 2 |
| #34037611 | 2 |
| #34037607 | 2 |
| #34037604 | 2 |
| #34037598 | 2 |
| #34037593 | 2 |
| #34037586 | 2 |
| D4×Dic587 | 2 |
| (C22⋊D587)⋊C4 | 2 |
| #34037579 | 2 |
| #34037577 | 2 |
| C2×C4×Dic587 | 2 |
| #123×C587 | 2 |
| #529 | 587 |