Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #27133834 | C2 | semidirect |
| 2. #27133832 | C2 | semidirect |
| 3. #27133828 | C2 | semidirect |
| 4. #27133823 | C2 | semidirect |
| 5. #27133821 | C2 | semidirect |
| 7. C4×Dic766 | C2 | semidirect |
| 8. C4×C22⋊D383 | C2 | semidirect |
| 9. #27133800 | C2 | semidirect |
| 10. C42×D383 | C2 | semidirect |
| 11. C4×D4×C383 | C2 | semidirect |
| 74. C383 | #529 | semidirect |
| 84. C4×D4 | D383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133834 | 2 |
| #27133832 | 2 |
| #27133828 | 2 |
| #27133823 | 2 |
| #27133821 | 2 |
| #27133812 | 2 |
| C4×Dic766 | 2 |
| C4×C22⋊D383 | 2 |
| #27133800 | 2 |
| C42×D383 | 2 |
| C4×D4×C383 | 2 |
| #529 | 383 |