Finite Group DatabasebetaFinite Group DatabasebetaOrder 38336.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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×D599 |
| commutator, socle, cosocle | C22×C599 | C24 |
| Fitting, prime radical | #121×C599 | C2 |
| hypercenter | #121 | D599 |
| hypocenter | C599 | #529 |
| LCS | G ▷ C22×C599 ▷ C599 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #34062708 | C2 | semidirect |
| 2. #34062706 | C2 | semidirect |
| 3. #34062702 | C2 | semidirect |
| 4. #34062696 | C2 | semidirect |
| 5. #34062694 | C2 | semidirect |
| 6. #34062680 | C2 | semidirect |
| 7. D4×Dic599 | C2 | semidirect |
| 8. D4×Dic599 | C2 | semidirect |
| 9. #34062671 | C2 | semidirect |
| 10. C2×C4×Dic599 | C2 | semidirect |
| 74. C599 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34062708 | 2 |
| #34062706 | 2 |
| #34062702 | 2 |
| #34062696 | 2 |
| #34062694 | 2 |
| #34062680 | 2 |
| D4×Dic599 | 2 |
| #34062671 | 2 |
| C2×C4×Dic599 | 2 |
| #121×C599 | 2 |
| #529 | 599 |