Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 149 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×#20259350 | C2 | semidirect |
| 2. #27133241 | C2 | semidirect |
| 3. #27133227 | C2 | semidirect |
| 4. #27132916 | C2 | semidirect |
| 5. #27132909 | C2 | semidirect |
| 6. #27132899 | C2 | semidirect |
| 7. #27132892 | C2 | semidirect |
| 8. #27132705 | C2 | semidirect |
| 9. #27132660 | C2 | semidirect |
| 10. C2×#20259244 | C2 | semidirect |
| 11. C2×#131×C191 | C2 | semidirect |
| 19. #20259301 | C22 | semidirect |
| 23. #20259296 | C22 | semidirect |
| 29. #20259256 | C22 | semidirect |
| 30. #20259254 | C22 | semidirect |
| 31. #20259247 | C22 | semidirect |
| 32. #20259247 | C22 | semidirect |
| 35. #20259244 | C22 | semidirect |
| 36. #20259244 | C22 | semidirect |
| 40. C2×M16×C191 | C22 | semidirect |
| 42. C22×C8×C191 | C22 | semidirect |
| 79. M16×C191 | D4 | semidirect |
| 151. C191 | #3062 | semidirect |
| 154. C2×#131 | D191 | semidirect |
| 172. C2×M16 | C2×D191 | semidirect |
| 174. C22×C8 | C2×D191 | semidirect |
| 220. M16 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259350 | 2 |
| #27133241 | 2 |
| #27133227 | 2 |
| #27132916 | 2 |
| #27132909 | 2 |
| #27132899 | 2 |
| #27132892 | 2 |
| #27132705 | 2 |
| #27132660 | 2 |
| C2×#20259244 | 2 |
| C2×#131×C191 | 2 |
| #3062 | 191 |