Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
134 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 55 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. C4×D796 | C2 | semidirect |
| 3. #20263888 | C2 | semidirect |
| 4. #20263876 | C2 | semidirect |
| 5. #20263875 | C2 | semidirect |
| 6. C4×C199⋊C8 | C2 | semidirect |
| 7. C4×D4×C199 | C2 | semidirect |
| 10. #15691871 | C4 | direct (N × H) |
| 22. D796 | C2×C4 | semidirect |
| 26. C199⋊C8 | C2×C4 | semidirect |
| 29. D4×C199 | C2×C4 | semidirect |
| 44. C4×C199 | D8 | semidirect |
| 53. C199 | C4×D8 | semidirect |
| 57. C4×D4 | D199 | semidirect |
| 79. D4 | C4×D199 | semidirect |
| 99. C4 | #15691871 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691871 | 2 |
| C4×D796 | 2 |
| #20263888 | 2 |
| #20263876 | 2 |
| #20263875 | 2 |
| C4×C199⋊C8 | 2 |
| C4×D4×C199 | 2 |
| C4×D8 | 199 |