Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#20259355 | C2 | semidirect |
| 3. C2×#20259310 | C2 | semidirect |
| 4. C4×#15690287 | C2 | semidirect |
| 5. #27132886 | C2 | semidirect |
| 6. #27132879 | C2 | semidirect |
| 7. #27132673 | C2 | semidirect |
| 8. #27132669 | C2 | semidirect |
| 9. #423×C191 | C2 | semidirect |
| 15. C2×Dic764 | C22 | semidirect |
| 17. C2×#15690276 | C22 | semidirect |
| 22. C4×Dic382 | C22 | semidirect |
| 23. C4×D764 | C22 | semidirect |
| 29. #20259247 | C22 | semidirect |
| 34. C4⋊C8×C191 | C22 | semidirect |
| 125. C191 | #3040 | semidirect |
| 133. #423 | D191 | semidirect |
| 158. 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×#20259355 | 2 |
| C2×#20259350 | 2 |
| C2×#20259310 | 2 |
| C4×#15690287 | 2 |
| #27132886 | 2 |
| #27132879 | 2 |
| #27132673 | 2 |
| #27132669 | 2 |
| #423×C191 | 2 |
| #3040 | 191 |