Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 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. #27133174 | C2 | semidirect |
| 2. #27133005 | C2 | semidirect |
| 3. #27132988 | C2 | semidirect |
| 4. #27132904 | C2 | semidirect |
| 5. #27132899 | C2 | semidirect |
| 6. #27132892 | C2 | semidirect |
| 7. #27132827 | C2 | semidirect |
| 8. #27132810 | C2 | semidirect |
| 9. C2×C22⋊C8×C191 | C2 | semidirect |
| 11. C2×Dic764 | C22 | semidirect |
| 12. C2×#15690276 | C22 | semidirect |
| 13. C2×D1528 | C22 | semidirect |
| 23. #20259256 | C22 | semidirect |
| 24. #20259256 | C22 | semidirect |
| 25. #20259254 | C22 | semidirect |
| 26. #20259247 | C22 | semidirect |
| 27. #20259247 | C22 | semidirect |
| 28. #20259244 | C22 | semidirect |
| 29. #20259244 | C22 | semidirect |
| 121. C191 | #3191 | semidirect |
| 131. C2×C22⋊C8 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133174 | 2 |
| #27133005 | 2 |
| #27132988 | 2 |
| #27132904 | 2 |
| #27132899 | 2 |
| #27132892 | 2 |
| #27132827 | 2 |
| #27132810 | 2 |
| C2×C22⋊C8×C191 | 2 |
| #3191 | 191 |