Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 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. #20263950 | C2 | semidirect |
| 2. #20263946 | C2 | semidirect |
| 3. #20263940 | C2 | semidirect |
| 4. #20263939 | C2 | semidirect |
| 5. #20263931 | C2 | semidirect |
| 7. (C22⋊D199)⋊C4 | C2 | semidirect |
| 8. C2×Dic199⋊C4 | C2 | semidirect |
| 9. C22⋊Q8×C199 | C2 | semidirect |
| 66. C199 | #539 | semidirect |
| 73. C22⋊Q8 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263950 | 2 |
| #20263946 | 2 |
| #20263940 | 2 |
| #20263939 | 2 |
| #20263931 | 2 |
| #20263929 | 2 |
| (C22⋊D199)⋊C4 | 2 |
| C2×Dic199⋊C4 | 2 |
| C22⋊Q8×C199 | 2 |
| #539 | 199 |