Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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. C2×#15691875 | C2 | semidirect |
| 3. #20263943 | C2 | semidirect |
| 4. C4×D796 | C2 | semidirect |
| 5. #20263880 | C2 | semidirect |
| 6. #20263877 | C2 | semidirect |
| 7. C4⋊C8×C199 | C2 | semidirect |
| 55. C199 | #463 | semidirect |
| 61. C4⋊C8 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691875 | 2 |
| C2×D1592 | 2 |
| #20263943 | 2 |
| C4×D796 | 2 |
| #20263880 | 2 |
| #20263877 | 2 |
| C4⋊C8×C199 | 2 |
| #463 | 199 |