Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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×#20259352 | C2 | semidirect |
| 2. C22×#15690275 | C2 | semidirect |
| 3. #27133140 | C2 | semidirect |
| 4. #27132882 | C2 | semidirect |
| 5. #27132860 | C2 | semidirect |
| 6. #27132690 | C2 | semidirect |
| 7. #27132668 | C2 | semidirect |
| 8. #27132659 | C2 | semidirect |
| 12. C2×#15690277 | C22 | semidirect |
| 15. C2×#15690275 | C22 | semidirect |
| 18. C4×Dic382 | C22 | semidirect |
| 22. C4⋊(C191⋊C8) | C22 | semidirect |
| 23. #20259246 | C22 | semidirect |
| 25. #20259243 | C22 | semidirect |
| 35. C2×Dic382 | D4 | semidirect |
| 116. C191 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259352 | 2 |
| C22×#15690275 | 2 |
| #27133140 | 2 |
| #27132882 | 2 |
| #27132860 | 2 |
| #27132690 | 2 |
| #27132668 | 2 |
| #27132659 | 2 |
| #535×C191 | 2 |
| #3043 | 191 |