Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
110 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 37 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 |
|---|---|---|
| 2. #20263946 | C2 | semidirect |
| 3. #20263877 | C2 | semidirect |
| 4. #20263876 | C2 | semidirect |
| 5. #20263875 | C2 | semidirect |
| 6. #20263865 | C2 | semidirect |
| 7. #102×C199 | C2 | semidirect |
| 52. C199 | #490 | semidirect |
| 59. #102 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263951 | 2 |
| #20263946 | 2 |
| #20263877 | 2 |
| #20263876 | 2 |
| #20263875 | 2 |
| #20263865 | 2 |
| #102×C199 | 2 |
| #490 | 199 |