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. #27133218 | C2 | semidirect |
| 3. #27132956 | C2 | semidirect |
| 4. #27132944 | C2 | semidirect |
| 5. #27132943 | C2 | semidirect |
| 6. #27132912 | C2 | semidirect |
| 7. #27132906 | C2 | semidirect |
| 8. #27132865 | C2 | semidirect |
| 9. #27132861 | C2 | semidirect |
| 10. #27132685 | C2 | semidirect |
| 11. #461×C191 | C2 | semidirect |
| 142. C191 | #3254 | semidirect |
| 152. #461 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133218 | 2 |
| #27133210 | 2 |
| #27132956 | 2 |
| #27132944 | 2 |
| #27132943 | 2 |
| #27132912 | 2 |
| #27132906 | 2 |
| #27132865 | 2 |
| #27132861 | 2 |
| #27132685 | 2 |
| #461×C191 | 2 |
| #3254 | 191 |