Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
266 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 149 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. #20263963 | C2 | semidirect |
| 3. #20263962 | C2 | semidirect |
| 4. #20263961 | C2 | semidirect |
| 5. M16×D199 | C2 | semidirect |
| 6. C2×C8×D199 | C2 | semidirect |
| 7. #131×C199 | C2 | semidirect |
| 14. #15691870 | C22 | semidirect |
| 15. #15691869 | C22 | semidirect |
| 16. C2×C199⋊C8 | C22 | semidirect |
| 19. C8×D199 | C22 | semidirect |
| 20. C8×D199 | C22 | semidirect |
| 22. M16×C199 | C22 | semidirect |
| 23. C2×C8×C199 | C22 | semidirect |
| 51. D199 | #131 | direct (N × H) |
| 52. C199 | C2×#131 | semidirect |
| 58. #131 | D199 | direct (N × H) |
| 70. M16 | C2×D199 | semidirect |
| 76. C2×C8 | C2×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D199 | 2 |
| #20263963 | 2 |
| #20263962 | 2 |
| #20263961 | 2 |
| M16×D199 | 2 |
| C2×C8×D199 | 2 |
| #131×C199 | 2 |
| C2×#131 | 199 |