Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
414 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 121 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×#20259301 | C2 | semidirect |
| 2. #27133004 | C2 | semidirect |
| 3. #27132996 | C2 | semidirect |
| 4. #27132979 | C2 | semidirect |
| 5. #27132919 | C2 | semidirect |
| 6. #27132907 | C2 | semidirect |
| 7. #27132825 | C2 | semidirect |
| 8. #27132818 | C2 | semidirect |
| 9. #27132801 | C2 | semidirect |
| 10. #27132627 | C2 | semidirect |
| 13. C2×#15690277 | C22 | semidirect |
| 14. C2×#15690275 | C22 | semidirect |
| 23. #20259255 | C22 | semidirect |
| 24. #20259253 | C22 | semidirect |
| 25. #20259246 | C22 | semidirect |
| 26. #20259245 | C22 | semidirect |
| 27. #20259245 | C22 | semidirect |
| 28. #20259243 | C22 | semidirect |
| 149. C191 | #3196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259301 | 2 |
| #27133004 | 2 |
| #27132996 | 2 |
| #27132979 | 2 |
| #27132919 | 2 |
| #27132907 | 2 |
| #27132825 | 2 |
| #27132818 | 2 |
| #27132801 | 2 |
| #27132627 | 2 |
| #525×C191 | 2 |
| #3196 | 191 |