Finite Group DatabasebetaFinite Group DatabasebetaOrder 33472.
218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 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×D523 |
| commutator, socle, cosocle | C22×C523 | C24 |
| Fitting | #123×C523 | C2 |
| prime radical | #30660344 | C2 |
| hypercenter | #123 | D523 |
| hypocenter | C523 | #539 |
| LCS | G ▷ C22×C523 ▷ C523 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30660366 | C2 | semidirect |
| 2. #30660366 | C2 | semidirect |
| 3. #30660364 | C2 | semidirect |
| 4. #30660363 | C2 | semidirect |
| 5. #30660355 | C2 | semidirect |
| 6. #30660355 | C2 | semidirect |
| 7. #30660354 | C2 | semidirect |
| 8. #30660352 | C2 | semidirect |
| 9. #30660351 | C2 | semidirect |
| 10. #30660350 | C2 | semidirect |
| 12. C4×C22⋊D523 | C2 | semidirect |
| 13. (C22⋊D523)⋊C4 | C2 | semidirect |
| 14. C4⋊C4×D523 | C2 | semidirect |
| 15. #123×C523 | C2 | semidirect |
| 103. C523 | #539 | semidirect |
| 112. #123 | D523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30660366 | 2 |
| #30660364 | 2 |
| #30660363 | 2 |
| #30660355 | 2 |
| #30660354 | 2 |
| #30660352 | 2 |
| #30660351 | 2 |
| #30660350 | 2 |
| #30660344 | 2 |
| C4×C22⋊D523 | 2 |
| (C22⋊D523)⋊C4 | 2 |
| C4⋊C4×D523 | 2 |
| #123×C523 | 2 |
| #539 | 523 |