Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×C4×Dic382 | C2 | semidirect |
| 3. #27132999 | C2 | semidirect |
| 5. #27132971 | C2 | semidirect |
| 6. #27132886 | C2 | semidirect |
| 7. #27132821 | C2 | semidirect |
| 9. #27132771 | C2 | semidirect |
| 10. #27132765 | C2 | semidirect |
| 11. #432×C191 | C2 | semidirect |
| 131. C191 | #3117 | semidirect |
| 143. #432 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133197 | 2 |
| C2×C4×Dic382 | 2 |
| #27132999 | 2 |
| #27132982 | 2 |
| #27132971 | 2 |
| #27132886 | 2 |
| #27132821 | 2 |
| #27132804 | 2 |
| #27132771 | 2 |
| #27132765 | 2 |
| #432×C191 | 2 |
| #3117 | 191 |