Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. #27133216 | C2 | semidirect |
| 3. #27133030 | C2 | semidirect |
| 4. #27133026 | C2 | semidirect |
| 5. #27133024 | C2 | semidirect |
| 6. #27133021 | C2 | semidirect |
| 7. #27132660 | C2 | semidirect |
| 8. #27132659 | C2 | semidirect |
| 9. #27132657 | C2 | semidirect |
| 10. C2×#20259232 | C2 | semidirect |
| 11. #416×C191 | C2 | semidirect |
| 125. C191 | #3135 | 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 |
| #27133030 | 2 |
| #27133026 | 2 |
| #27133024 | 2 |
| #27133021 | 2 |
| #27132660 | 2 |
| #27132659 | 2 |
| #27132657 | 2 |
| C2×#20259232 | 2 |
| #416×C191 | 2 |
| #3135 | 191 |