Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#20259347 | C2 | semidirect |
| 2. C22×D1528 | C2 | semidirect |
| 3. #27133227 | C2 | semidirect |
| 4. #27133137 | C2 | semidirect |
| 5. #27132881 | C2 | semidirect |
| 6. #27132857 | C2 | semidirect |
| 7. #27132689 | C2 | semidirect |
| 8. #27132667 | C2 | semidirect |
| 9. #416×C191 | C2 | semidirect |
| 13. C2×#15690274 | C22 | semidirect |
| 16. C2×#15690272 | C22 | semidirect |
| 18. #20259318 | C22 | semidirect |
| 19. #20259311 | C22 | semidirect |
| 23. #20259284 | C22 | semidirect |
| 26. Dic191⋊C8 | C22 | semidirect |
| 27. #20259242 | C22 | semidirect |
| 31. #103×C191 | C22 | semidirect |
| 32. #102×C191 | C22 | semidirect |
| 40. C2×D764 | D4 | semidirect |
| 121. C191 | #3041 | semidirect |
| 131. #416 | D191 | semidirect |
| 152. #103 | C2×D191 | semidirect |
| 154. #102 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259347 | 2 |
| C22×D1528 | 2 |
| #27133227 | 2 |
| #27133137 | 2 |
| #27132881 | 2 |
| #27132857 | 2 |
| #27132689 | 2 |
| #27132667 | 2 |
| #416×C191 | 2 |
| #3041 | 191 |