Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27133291 | C2 | semidirect |
| 2. #27133027 | C2 | semidirect |
| 3. #27133022 | C2 | semidirect |
| 4. #27133017 | C2 | semidirect |
| 5. #27133009 | C2 | semidirect |
| 6. #27132668 | C2 | semidirect |
| 7. #27132664 | C2 | semidirect |
| 8. #27132659 | C2 | semidirect |
| 9. C2×#20259243 | C2 | semidirect |
| 10. #27132619 | C2 | semidirect |
| 14. #20259322 | C22 | semidirect |
| 16. #20259314 | C22 | semidirect |
| 21. #20259246 | C22 | semidirect |
| 22. #20259246 | C22 | semidirect |
| 23. #20259246 | C22 | semidirect |
| 28. #20259243 | C22 | semidirect |
| 29. #20259243 | C22 | semidirect |
| 30. #20259243 | C22 | semidirect |
| 31. #20259233 | C22 | semidirect |
| 32. C4×C191⋊C8 | C22 | semidirect |
| 135. C191 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133291 | 2 |
| #27133027 | 2 |
| #27133022 | 2 |
| #27133017 | 2 |
| #27133009 | 2 |
| #27132668 | 2 |
| #27132664 | 2 |
| #27132659 | 2 |
| C2×#20259243 | 2 |
| #27132619 | 2 |
| #535×C191 | 2 |
| #3136 | 191 |