Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. C4×Dic766 | C2 | semidirect |
| 3. #27133774 | C2 | semidirect |
| 4. #27133764 | C2 | semidirect |
| 6. #27133752 | C2 | semidirect |
| 9. #20259445 | C4 | semidirect |
| 21. Dic766 | C2×C4 | semidirect |
| 25. C383⋊C8 | C2×C4 | semidirect |
| 49. C383 | #440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259445 | 2 |
| C4×Dic766 | 2 |
| #27133774 | 2 |
| #27133764 | 2 |
| #27133762 | 2 |
| #27133752 | 2 |
| C4×D4×C383 | 2 |
| #440 | 383 |