Finite Group DatabasebetaFinite Group DatabasebetaOrder 33472.
240 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 240 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×D523 |
| commutator, socle, cosocle | C22×C523 | C24 |
| Fitting | #121×C523 | C2 |
| hypercenter | #121 | D523 |
| hypocenter | C523 | #540 |
| LCS | G ▷ C22×C523 ▷ C523 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30660369 | C2 | semidirect |
| 2. #30660364 | C2 | semidirect |
| 3. #30660357 | C2 | semidirect |
| 4. #30660355 | C2 | semidirect |
| 5. #30660347 | C2 | semidirect |
| 6. #30660345 | C2 | semidirect |
| 7. #30660344 | C2 | semidirect |
| 8. D4×Dic523 | C2 | semidirect |
| 9. #30660335 | C2 | semidirect |
| 10. #30660332 | C2 | semidirect |
| 11. #121×C523 | C2 | semidirect |
| 79. C523 | #540 | semidirect |
| 88. #121 | D523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30660369 | 2 |
| #30660364 | 2 |
| #30660357 | 2 |
| #30660355 | 2 |
| #30660347 | 2 |
| #30660345 | 2 |
| #30660344 | 2 |
| D4×Dic523 | 2 |
| #30660335 | 2 |
| #30660332 | 2 |
| #121×C523 | 2 |
| #540 | 523 |