Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27133197 | C2 | semidirect |
| 2. C2×C4×D764 | C2 | semidirect |
| 3. #27132994 | C2 | semidirect |
| 4. #27132977 | C2 | semidirect |
| 5. #27132964 | C2 | semidirect |
| 6. #27132879 | C2 | semidirect |
| 7. #27132816 | C2 | semidirect |
| 9. #27132776 | C2 | semidirect |
| 10. #27132765 | C2 | semidirect |
| 11. #432×C191 | C2 | semidirect |
| 17. #20259314 | C22 | semidirect |
| 18. #20259310 | C22 | semidirect |
| 22. C4×Dic382 | C22 | semidirect |
| 27. C4×D764 | C22 | semidirect |
| 32. #20259256 | C22 | semidirect |
| 33. #20259254 | C22 | semidirect |
| 34. #20259247 | C22 | semidirect |
| 37. #20259244 | C22 | semidirect |
| 39. C4⋊C8×C191 | C22 | semidirect |
| 42. #97×C191 | C22 | semidirect |
| 140. C191 | #3114 | semidirect |
| 152. #432 | D191 | semidirect |
| 176. C4⋊C8 | C2×D191 | semidirect |
| 183. #97 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133197 | 2 |
| C2×C4×D764 | 2 |
| #27132994 | 2 |
| #27132977 | 2 |
| #27132964 | 2 |
| #27132879 | 2 |
| #27132816 | 2 |
| #27132799 | 2 |
| #27132776 | 2 |
| #27132765 | 2 |
| #432×C191 | 2 |
| #3114 | 191 |