Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#20259344 | C2 | semidirect |
| 3. #27133232 | C2 | semidirect |
| 4. #27133143 | C2 | semidirect |
| 5. #27132886 | C2 | semidirect |
| 6. #27132879 | C2 | semidirect |
| 7. #27132864 | C2 | semidirect |
| 8. #27132859 | C2 | semidirect |
| 9. #27132665 | C2 | semidirect |
| 10. C2×#20259244 | C2 | semidirect |
| 11. #424×C191 | C2 | semidirect |
| 17. C2×Dic764 | C22 | semidirect |
| 19. C2×#15690276 | C22 | semidirect |
| 20. C2×#15690276 | C22 | semidirect |
| 22. C2×D1528 | C22 | semidirect |
| 28. C4×Dic382 | C22 | semidirect |
| 29. C4×D764 | C22 | semidirect |
| 34. #20259247 | C22 | semidirect |
| 37. #20259244 | C22 | semidirect |
| 41. C4⋊C8×C191 | C22 | semidirect |
| 42. C4⋊C8×C191 | C22 | semidirect |
| 47. #15690287 | D4 | semidirect |
| 154. C191 | #3045 | semidirect |
| 164. #424 | D191 | semidirect |
| 192. C4⋊C8 | C2×D191 | semidirect |
| 193. 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 |
| C2×#20259344 | 2 |
| #27133232 | 2 |
| #27133143 | 2 |
| #27132886 | 2 |
| #27132879 | 2 |
| #27132864 | 2 |
| #27132859 | 2 |
| #27132665 | 2 |
| C2×#20259244 | 2 |
| #424×C191 | 2 |
| #3045 | 191 |