Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×#15691870 | C2 | semidirect |
| 3. #20263871 | C2 | direct (N × H) |
| 4. C2×M16×C199 | C2 | semidirect |
| 13. #15691870 | C22 | semidirect |
| 17. M16×C199 | C22 | semidirect |
| 50. C2×C199 | #100 | semidirect |
| 53. C199 | C2×#100 | semidirect |
| 57. C2×M16 | D199 | semidirect |
| 70. M16 | C2×D199 | semidirect |
| 105. C2 | #20263871 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D796 | 2 |
| C2×#15691870 | 2 |
| #20263871 | 2 |
| C2×M16×C199 | 2 |
| C2×#100 | 199 |