Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20263954 | C2 | semidirect |
| 2. #20263953 | C2 | semidirect |
| 3. #20263950 | C2 | semidirect |
| 4. #20263950 | C2 | semidirect |
| 5. #20263948 | C2 | semidirect |
| 6. #20263948 | C2 | semidirect |
| 7. #20263946 | C2 | semidirect |
| 8. #20263945 | C2 | semidirect |
| 12. #20263934 | C2 | semidirect |
| 13. #20263933 | C2 | semidirect |
| 14. #20263931 | C2 | semidirect |
| 15. C22⋊Q8×C199 | C2 | semidirect |
| 97. C199 | #563 | semidirect |
| 113. C22⋊Q8 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263954 | 2 |
| #20263953 | 2 |
| #20263950 | 2 |
| #20263948 | 2 |
| #20263946 | 2 |
| #20263945 | 2 |
| #20263941 | 2 |
| #20263938 | 2 |
| #20263937 | 2 |
| #20263934 | 2 |
| #20263933 | 2 |
| #20263931 | 2 |
| C22⋊Q8×C199 | 2 |
| #563 | 199 |