Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 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. #27133887 | C2 | semidirect |
| 2. #27133872 | C2 | semidirect |
| 3. #27133866 | C2 | semidirect |
| 4. #27133861 | C2 | semidirect |
| 5. C2×#20259444 | C2 | semidirect |
| 6. #27133848 | C2 | semidirect |
| 7. 2−1+4×C383 | C2 | semidirect |
| 12. #20259447 | C22 | semidirect |
| 13. #20259445 | C22 | semidirect |
| 14. #20259444 | C22 | semidirect |
| 15. #20259444 | C22 | semidirect |
| 16. #20259442 | C22 | semidirect |
| 17. #20259441 | C22 | semidirect |
| 18. C2×C383⋊C8 | C22 | semidirect |
| 21. #41×C383 | C22 | semidirect |
| 23. C2×Q8×C383 | C22 | semidirect |
| 53. C383 | #577 | semidirect |
| 55. 2−1+4 | D383 | semidirect |
| 66. #41 | C2×D383 | semidirect |
| 68. C2×Q8 | C2×D383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133887 | 2 |
| #27133872 | 2 |
| #27133866 | 2 |
| #27133861 | 2 |
| C2×#20259444 | 2 |
| #27133848 | 2 |
| 2−1+4×C383 | 2 |
| #577 | 383 |