Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20259355 | C2 | semidirect |
| 3. #27133239 | C2 | semidirect |
| 4. #27133143 | C2 | semidirect |
| 5. #27132886 | C2 | semidirect |
| 6. #27132879 | C2 | semidirect |
| 7. #27132874 | C2 | semidirect |
| 8. #27132869 | C2 | semidirect |
| 9. #27132665 | C2 | semidirect |
| 10. C2×#20259247 | C2 | semidirect |
| 11. #424×C191 | C2 | semidirect |
| 146. C191 | #3046 | semidirect |
| 156. #424 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259355 | 2 |
| C2×#20259344 | 2 |
| #27133239 | 2 |
| #27133143 | 2 |
| #27132886 | 2 |
| #27132879 | 2 |
| #27132874 | 2 |
| #27132869 | 2 |
| #27132665 | 2 |
| C2×#20259247 | 2 |
| #424×C191 | 2 |
| #3046 | 191 |