Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20263950 | C2 | semidirect |
| 3. #20263944 | C2 | semidirect |
| 4. #20263941 | C2 | semidirect |
| 5. #20263937 | C2 | semidirect |
| 6. #20263935 | C2 | semidirect |
| 8. Q8×Dic199 | C2 | semidirect |
| 9. #20263917 | C2 | semidirect |
| 10. #20263914 | C2 | semidirect |
| 11. C22⋊Q8×C199 | C2 | semidirect |
| 73. C199 | #542 | semidirect |
| 81. 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 |
| #20263950 | 2 |
| #20263944 | 2 |
| #20263941 | 2 |
| #20263937 | 2 |
| #20263935 | 2 |
| #20263929 | 2 |
| Q8×Dic199 | 2 |
| #20263917 | 2 |
| #20263914 | 2 |
| C22⋊Q8×C199 | 2 |
| #542 | 199 |