Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 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 | C2×C22⋊C4×C383 | C2 |
| hypercenter | C2×C22⋊C4 | D383 |
| hypocenter | C383 | #538 |
| LCS | G ▷ C22×C383 ▷ C383 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27133834 | C2 | semidirect |
| 2. #27133827 | C2 | semidirect |
| 3. #27133823 | C2 | semidirect |
| 4. #27133820 | C2 | semidirect |
| 5. #27133815 | C2 | semidirect |
| 6. #27133814 | C2 | semidirect |
| 7. #27133810 | C2 | semidirect |
| 8. C4×C22⋊D383 | C2 | semidirect |
| 9. C2×C22⋊C4×C383 | C2 | semidirect |
| 10. C2×Dic766 | C22 | semidirect |
| 11. C2×D1532 | C22 | semidirect |
| 15. C2×C4×D383 | C22 | semidirect |
| 16. C4⋊Dic383 | C22 | semidirect |
| 17. C4⋊Dic383 | C22 | semidirect |
| 18. Dic383⋊C4 | C22 | semidirect |
| 19. Dic383⋊C4 | C22 | semidirect |
| 23. (C2×D383)⋊C4 | C22 | semidirect |
| 24. (C2×D383)⋊C4 | C22 | semidirect |
| 25. C4×Dic383 | C22 | semidirect |
| 74. C383 | #538 | semidirect |
| 84. C2×C22⋊C4 | D383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133834 | 2 |
| #27133827 | 2 |
| #27133823 | 2 |
| #27133820 | 2 |
| #27133815 | 2 |
| #27133814 | 2 |
| #27133810 | 2 |
| C4×C22⋊D383 | 2 |
| C2×C22⋊C4×C383 | 2 |
| #538 | 383 |