Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 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 |
|---|---|---|
| 1. C2×#15691886 | C2 | semidirect |
| 2. #20263981 | C2 | direct (N × H) |
| 3. C2×#15691874 | C2 | semidirect |
| 4. C2×#15691871 | C2 | semidirect |
| 5. C2×#15691870 | C2 | semidirect |
| 6. C22×D4×C199 | C2 | semidirect |
| 8. #15691886 | C22 | semidirect |
| 9. C2×Dic398 | C22 | semidirect |
| 10. C2×D796 | C22 | semidirect |
| 13. #15691874 | C22 | semidirect |
| 14. #15691871 | C22 | semidirect |
| 15. #15691870 | C22 | semidirect |
| 16. C2×C199⋊C8 | C22 | semidirect |
| 21. C2×D4×C199 | C22 | semidirect |
| 25. Dic398 | C23 | semidirect |
| 27. D796 | C23 | semidirect |
| 31. C199⋊C8 | C23 | semidirect |
| 57. C2×C199 | AGL(1,ℤ/8) | semidirect |
| 60. C199 | C2×AGL(1,ℤ/8) | semidirect |
| 63. C22×D4 | D199 | semidirect |
| 77. C2×D4 | C2×D199 | semidirect |
| 119. C2 | #20263981 | 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 |
| #20263981 | 2 |
| C2×#15691874 | 2 |
| C2×#15691871 | 2 |
| C2×#15691870 | 2 |
| C22×D4×C199 | 2 |
| C2×AGL(1,ℤ/8) | 199 |