Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#20259456 | C2 | semidirect |
| 2. C2×#20259445 | C2 | semidirect |
| 3. #27133812 | C2 | semidirect |
| 4. #27133766 | C2 | semidirect |
| 5. #27133762 | C2 | semidirect |
| 6. (C2×D383)⋊C8 | C2 | semidirect |
| 7. C2×D8×C383 | C2 | semidirect |
| 25. Dic766 | D4 | semidirect |
| 40. D4×C383 | D4 | semidirect |
| 64. C383 | #449 | semidirect |
| 68. C2×D8 | D383 | semidirect |
| 98. D4 | C22⋊D383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259456 | 2 |
| C2×#20259445 | 2 |
| #27133812 | 2 |
| #27133766 | 2 |
| #27133762 | 2 |
| (C2×D383)⋊C8 | 2 |
| C2×D8×C383 | 2 |
| #449 | 383 |