Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
| 2. #20263934 | C2 | semidirect |
| 4. #20263889 | C2 | semidirect |
| 5. #20263880 | C2 | semidirect |
| 6. #20263877 | C2 | semidirect |
| 7. C2×M16×C199 | C2 | semidirect |
| 36. C8×C199 | D4 | semidirect |
| 55. C199 | #468 | semidirect |
| 58. C2×M16 | D199 | semidirect |
| 92. C8 | C22⋊D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691875 | 2 |
| #20263934 | 2 |
| #20263929 | 2 |
| #20263889 | 2 |
| #20263880 | 2 |
| #20263877 | 2 |
| C2×M16×C199 | 2 |
| #468 | 199 |