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. #27133836 | C2 | semidirect |
| 2. #27133832 | C2 | semidirect |
| 3. #27133830 | C2 | semidirect |
| 4. #27133825 | C2 | semidirect |
| 6. Q8×Dic383 | C2 | semidirect |
| 7. #27133803 | C2 | semidirect |
| 8. (C22⋊D383)⋊C4 | C2 | semidirect |
| 9. #27133799 | C2 | semidirect |
| 10. C2×C4×Dic383 | C2 | semidirect |
| 11. C22⋊Q8×C383 | C2 | semidirect |
| 74. C383 | #529 | semidirect |
| 80. C22⋊Q8 | D383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133836 | 2 |
| #27133832 | 2 |
| #27133830 | 2 |
| #27133825 | 2 |
| #27133815 | 2 |
| Q8×Dic383 | 2 |
| #27133803 | 2 |
| (C22⋊D383)⋊C4 | 2 |
| #27133799 | 2 |
| C2×C4×Dic383 | 2 |
| C22⋊Q8×C383 | 2 |
| #529 | 383 |