Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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. C22×Dic398 | C2 | semidirect |
| 3. #20263988 | C2 | direct (N × H) |
| 4. C2×Dic796 | C2 | semidirect |
| 5. C2×#15691875 | C2 | semidirect |
| 6. C2×M16×C199 | C2 | semidirect |
| 13. C2×Dic398 | C22 | semidirect |
| 18. Dic796 | C22 | semidirect |
| 19. #15691875 | C22 | semidirect |
| 21. M16×C199 | C22 | semidirect |
| 53. C2×C199 | #137 | semidirect |
| 56. C199 | C2×#137 | semidirect |
| 63. C2×M16 | D199 | semidirect |
| 78. M16 | C2×D199 | semidirect |
| 111. C2 | #20263988 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691886 | 2 |
| C22×Dic398 | 2 |
| #20263988 | 2 |
| C2×Dic796 | 2 |
| C2×#15691875 | 2 |
| C2×M16×C199 | 2 |
| C2×#137 | 199 |