Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×D1528 | C2 | semidirect |
| 3. #27133232 | C2 | semidirect |
| 4. #27133137 | C2 | semidirect |
| 5. #27132879 | C2 | semidirect |
| 6. #27132859 | C2 | semidirect |
| 7. #27132669 | C2 | semidirect |
| 8. #27132660 | C2 | semidirect |
| 9. #424×C191 | C2 | semidirect |
| 14. C2×#15690276 | C22 | semidirect |
| 17. C2×D1528 | C22 | semidirect |
| 18. #20259319 | C22 | semidirect |
| 19. #20259310 | C22 | semidirect |
| 22. C4×D764 | C22 | semidirect |
| 26. #20259247 | C22 | semidirect |
| 27. #20259244 | C22 | semidirect |
| 28. #20259244 | C22 | semidirect |
| 32. C4⋊C8×C191 | C22 | semidirect |
| 44. C2×D764 | D4 | semidirect |
| 121. C191 | #3041 | semidirect |
| 129. #424 | D191 | semidirect |
| 151. C4⋊C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259350 | 2 |
| C22×D1528 | 2 |
| #27133232 | 2 |
| #27133137 | 2 |
| #27132879 | 2 |
| #27132859 | 2 |
| #27132669 | 2 |
| #27132660 | 2 |
| #424×C191 | 2 |
| #3041 | 191 |