Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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×#15691886 | C2 | semidirect |
| 2. #20263988 | C2 | semidirect |
| 3. #20263983 | C2 | semidirect |
| 4. #20263977 | C2 | semidirect |
| 5. C2×M16×C199 | C2 | semidirect |
| 9. #15691886 | C22 | semidirect |
| 10. C2×Dic398 | C22 | semidirect |
| 11. C2×D796 | C22 | semidirect |
| 14. Dic796 | C22 | semidirect |
| 15. #15691875 | C22 | semidirect |
| 16. D1592 | C22 | semidirect |
| 18. M16×C199 | C22 | semidirect |
| 19. C2×C8×C199 | C22 | semidirect |
| 49. C199 | #575 | semidirect |
| 55. C2×M16 | D199 | semidirect |
| 68. M16 | C2×D199 | semidirect |
| 69. C2×C8 | C2×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691886 | 2 |
| #20263988 | 2 |
| #20263983 | 2 |
| #20263977 | 2 |
| C2×M16×C199 | 2 |
| #575 | 199 |