Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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. #27133836 | C2 | semidirect |
| 2. #27133834 | C2 | semidirect |
| 3. #27133831 | C2 | semidirect |
| 4. #27133827 | C2 | semidirect |
| 5. #27133826 | C2 | semidirect |
| 6. #27133823 | C2 | semidirect |
| 7. #27133819 | C2 | semidirect |
| 9. C4×Dic766 | C2 | semidirect |
| 10. C4×D1532 | C2 | semidirect |
| 11. C4×C22⋊D383 | C2 | semidirect |
| 12. C4×C22⋊D383 | C2 | semidirect |
| 13. #27133798 | C2 | semidirect |
| 14. C42×D383 | C2 | semidirect |
| 15. #117×C383 | C2 | semidirect |
| 103. C383 | #529 | semidirect |
| 118. #117 | D383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133836 | 2 |
| #27133834 | 2 |
| #27133831 | 2 |
| #27133827 | 2 |
| #27133826 | 2 |
| #27133823 | 2 |
| #27133819 | 2 |
| #27133814 | 2 |
| C4×Dic766 | 2 |
| C4×D1532 | 2 |
| C4×C22⋊D383 | 2 |
| #27133798 | 2 |
| C42×D383 | 2 |
| #117×C383 | 2 |
| #529 | 383 |