Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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. #27132679 | C2 | semidirect |
| 3. #27132659 | C2 | semidirect |
| 4. #27132657 | C2 | semidirect |
| 5. #27132636 | C2 | semidirect |
| 6. #27132631 | C2 | semidirect |
| 7. #421×C191 | C2 | semidirect |
| 10. #20259369 | C4 | semidirect |
| 12. #20259368 | C4 | semidirect |
| 20. C22×C191⋊C8 | C22 | semidirect |
| 21. #20259281 | C22 | semidirect |
| 30. C2×M16×C191 | C22 | semidirect |
| 31. #117×C191 | C22 | semidirect |
| 166. C191 | #1794 | semidirect |
| 170. #421 | D191 | semidirect |
| 188. C2×M16 | C2×D191 | semidirect |
| 191. #117 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133499 | 2 |
| #27132679 | 2 |
| #27132659 | 2 |
| #27132657 | 2 |
| #27132636 | 2 |
| #27132631 | 2 |
| #421×C191 | 2 |
| #1794 | 191 |