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 |
|---|---|---|
| 2. C2×#20259313 | C2 | semidirect |
| 3. #27133030 | C2 | semidirect |
| 4. #27133026 | C2 | semidirect |
| 5. #27133019 | C2 | semidirect |
| 6. #27133016 | C2 | semidirect |
| 7. #27132665 | C2 | semidirect |
| 8. #27132664 | C2 | semidirect |
| 9. #27132662 | C2 | semidirect |
| 10. M16×Dic191 | C2 | semidirect |
| 11. #417×C191 | C2 | semidirect |
| 146. C191 | #3142 | semidirect |
| 157. #417 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133209 | 2 |
| C2×#20259313 | 2 |
| #27133030 | 2 |
| #27133026 | 2 |
| #27133019 | 2 |
| #27133016 | 2 |
| #27132665 | 2 |
| #27132664 | 2 |
| #27132662 | 2 |
| M16×Dic191 | 2 |
| #417×C191 | 2 |
| #3142 | 191 |