Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20263944 | C2 | semidirect |
| 4. #20263940 | C2 | semidirect |
| 5. #20263931 | C2 | semidirect |
| 7. C4×D796 | C2 | semidirect |
| 8. C4×D796 | C2 | semidirect |
| 9. #20263912 | C2 | semidirect |
| 10. C42×D199 | C2 | semidirect |
| 11. C4×Q8×C199 | C2 | semidirect |
| 74. C199 | #529 | semidirect |
| 82. C4×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 |
| #20263944 | 2 |
| #20263940 | 2 |
| #20263931 | 2 |
| #20263930 | 2 |
| C4×D796 | 2 |
| #20263912 | 2 |
| C42×D199 | 2 |
| C4×Q8×C199 | 2 |
| #529 | 199 |