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×#20259348 | C2 | semidirect |
| 2. C2×#20259342 | C2 | semidirect |
| 3. #27133143 | C2 | semidirect |
| 4. #27132882 | C2 | semidirect |
| 5. #27132875 | C2 | semidirect |
| 6. #27132860 | C2 | semidirect |
| 7. #27132855 | C2 | semidirect |
| 8. #27132690 | C2 | semidirect |
| 9. #27132664 | C2 | semidirect |
| 10. C2×#20259243 | C2 | semidirect |
| 11. #535×C191 | C2 | semidirect |
| 15. C2×#15690277 | C22 | semidirect |
| 17. C2×#15690275 | C22 | semidirect |
| 18. C2×#15690274 | C22 | semidirect |
| 20. C2×#15690272 | C22 | semidirect |
| 23. C4×Dic382 | C22 | semidirect |
| 24. C4×D764 | C22 | semidirect |
| 29. C4⋊(C191⋊C8) | C22 | semidirect |
| 30. C4⋊(C191⋊C8) | C22 | semidirect |
| 31. #20259246 | C22 | semidirect |
| 34. #20259243 | C22 | semidirect |
| 44. #15690287 | D4 | semidirect |
| 154. C191 | #3045 | semidirect |
| 158. #535 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259348 | 2 |
| C2×#20259342 | 2 |
| #27133143 | 2 |
| #27132882 | 2 |
| #27132875 | 2 |
| #27132860 | 2 |
| #27132855 | 2 |
| #27132690 | 2 |
| #27132664 | 2 |
| C2×#20259243 | 2 |
| #535×C191 | 2 |
| #3045 | 191 |