Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
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×D383 |
| commutator, socle, cosocle | C22×C383 | C24 |
| Fitting | C4×D4×C383 | C2 |
| hypercenter | C4×D4 | D383 |
| hypocenter | C383 | #540 |
| LCS | G ▷ C22×C383 ▷ C383 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27133837 | C2 | semidirect |
| 2. #27133832 | C2 | semidirect |
| 3. #27133824 | C2 | semidirect |
| 4. #27133823 | C2 | semidirect |
| 5. #27133816 | C2 | semidirect |
| 6. #27133815 | C2 | semidirect |
| 7. #27133814 | C2 | semidirect |
| 8. #27133812 | C2 | semidirect |
| 9. C4×D1532 | C2 | semidirect |
| 10. #27133798 | C2 | semidirect |
| 11. C4×D4×C383 | C2 | semidirect |
| 79. C383 | #540 | semidirect |
| 90. C4×D4 | D383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133837 | 2 |
| #27133832 | 2 |
| #27133824 | 2 |
| #27133823 | 2 |
| #27133816 | 2 |
| #27133815 | 2 |
| #27133814 | 2 |
| #27133812 | 2 |
| C4×D1532 | 2 |
| #27133798 | 2 |
| C4×D4×C383 | 2 |
| #540 | 383 |