Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20259457 | C2 | semidirect |
| 2. #27133874 | C2 | semidirect |
| 3. #27133869 | C2 | semidirect |
| 4. #27133863 | C2 | semidirect |
| 5. C2×M16×C383 | C2 | semidirect |
| 9. #20259457 | C22 | semidirect |
| 10. C2×Dic766 | C22 | semidirect |
| 11. C2×D1532 | C22 | semidirect |
| 14. Dic1532 | C22 | semidirect |
| 15. #20259446 | C22 | semidirect |
| 16. D3064 | C22 | semidirect |
| 18. M16×C383 | C22 | semidirect |
| 19. C2×C8×C383 | C22 | semidirect |
| 49. C383 | #575 | semidirect |
| 55. C2×M16 | D383 | semidirect |
| 68. M16 | C2×D383 | semidirect |
| 69. C2×C8 | C2×D383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259457 | 2 |
| #27133874 | 2 |
| #27133869 | 2 |
| #27133863 | 2 |
| C2×M16×C383 | 2 |
| #575 | 383 |