Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 129 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. #27133216 | C2 | semidirect |
| 3. #27133019 | C2 | semidirect |
| 4. #27133016 | C2 | semidirect |
| 5. #27133012 | C2 | semidirect |
| 6. #27133008 | C2 | semidirect |
| 7. #27132660 | C2 | semidirect |
| 8. #27132659 | C2 | semidirect |
| 9. #27132657 | C2 | semidirect |
| 10. C2×C8×Dic191 | C2 | semidirect |
| 11. #416×C191 | C2 | semidirect |
| 125. C191 | #3131 | semidirect |
| 136. #416 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133216 | 2 |
| #27133209 | 2 |
| #27133019 | 2 |
| #27133016 | 2 |
| #27133012 | 2 |
| #27133008 | 2 |
| #27132660 | 2 |
| #27132659 | 2 |
| #27132657 | 2 |
| C2×C8×Dic191 | 2 |
| #416×C191 | 2 |
| #3131 | 191 |