Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 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. #20264002 | C2 | semidirect |
| 2. #20264001 | C2 | semidirect |
| 3. #20263988 | C2 | semidirect |
| 4. #20263983 | C2 | semidirect |
| 5. #20263977 | C2 | semidirect |
| 6. C2×#15691875 | C2 | semidirect |
| 7. #131×C199 | C2 | semidirect |
| 10. #15691886 | C22 | semidirect |
| 12. C2×Dic398 | C22 | semidirect |
| 16. Dic796 | C22 | semidirect |
| 17. #15691875 | C22 | semidirect |
| 18. #15691875 | C22 | semidirect |
| 19. #15691875 | C22 | semidirect |
| 20. D1592 | C22 | semidirect |
| 22. M16×C199 | C22 | semidirect |
| 23. C2×C8×C199 | C22 | semidirect |
| 53. C199 | #577 | semidirect |
| 61. #131 | D199 | semidirect |
| 76. M16 | C2×D199 | semidirect |
| 77. C2×C8 | C2×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20264002 | 2 |
| #20264001 | 2 |
| #20263988 | 2 |
| #20263983 | 2 |
| #20263977 | 2 |
| C2×#15691875 | 2 |
| #131×C199 | 2 |
| #577 | 199 |