Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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. #27133866 | C2 | semidirect |
| 2. C2×#20259442 | C2 | semidirect |
| 3. #27133848 | C2 | semidirect |
| 4. #27133776 | C2 | semidirect |
| 5. #27133758 | C2 | semidirect |
| 6. #27133757 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C383 | C2 | semidirect |
| 53. C383 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133866 | 2 |
| C2×#20259442 | 2 |
| #27133848 | 2 |
| #27133776 | 2 |
| #27133758 | 2 |
| #27133757 | 2 |
| AGL(1,ℤ/8)×C383 | 2 |
| #472 | 383 |