Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #27133266 | C2 | semidirect |
| 2. #27133064 | C2 | semidirect |
| 3. #27133038 | C2 | semidirect |
| 4. #27133026 | C2 | semidirect |
| 5. #27132914 | C2 | semidirect |
| 6. #27132899 | C2 | semidirect |
| 7. #27132772 | C2 | semidirect |
| 8. D8×Dic191 | C2 | semidirect |
| 9. #27132745 | C2 | semidirect |
| 10. #27132618 | C2 | semidirect |
| 11. #466×C191 | C2 | semidirect |
| 123. C191 | #3176 | semidirect |
| 131. #466 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133266 | 2 |
| #27133064 | 2 |
| #27133038 | 2 |
| #27133026 | 2 |
| #27132914 | 2 |
| #27132899 | 2 |
| #27132772 | 2 |
| D8×Dic191 | 2 |
| #27132745 | 2 |
| #27132618 | 2 |
| #466×C191 | 2 |
| #3176 | 191 |