Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #27133461 | C2 | semidirect |
| 2. C2×#20259350 | C2 | semidirect |
| 3. C2×#20259347 | C2 | semidirect |
| 4. #27132933 | C2 | semidirect |
| 5. #27132926 | C2 | semidirect |
| 6. #27132712 | C2 | semidirect |
| 7. #27132645 | C2 | semidirect |
| 8. C2×#20259238 | C2 | semidirect |
| 9. #568×C191 | C2 | semidirect |
| 13. #20259352 | C22 | semidirect |
| 19. #20259347 | C22 | semidirect |
| 21. C2×#15690276 | C22 | semidirect |
| 23. C2×D1528 | C22 | semidirect |
| 27. #20259258 | C22 | semidirect |
| 28. #20259240 | C22 | semidirect |
| 29. #20259238 | C22 | semidirect |
| 30. #20259238 | C22 | semidirect |
| 33. #131×C191 | C22 | semidirect |
| 147. C191 | #3068 | semidirect |
| 152. #568 | D191 | semidirect |
| 175. #131 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133461 | 2 |
| C2×#20259350 | 2 |
| C2×#20259347 | 2 |
| #27132933 | 2 |
| #27132926 | 2 |
| #27132712 | 2 |
| #27132645 | 2 |
| C2×#20259238 | 2 |
| #568×C191 | 2 |
| #3068 | 191 |