Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 51 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×#15691871 | C2 | semidirect |
| 2. #20263929 | C2 | semidirect |
| 3. #20263876 | C2 | semidirect |
| 4. C22⋊(C199⋊C8) | C2 | semidirect |
| 5. C22×D4×C199 | C2 | semidirect |
| 6. C2×D796 | C22 | semidirect |
| 9. C2×C199⋊C8 | C22 | semidirect |
| 10. C4⋊Dic199 | C22 | semidirect |
| 29. D4×C199 | D4 | semidirect |
| 39. C22×C199 | D8 | semidirect |
| 53. C199 | #447 | semidirect |
| 55. C22×D4 | D199 | semidirect |
| 81. D4 | C22⋊D199 | semidirect |
| 96. C22 | #15691871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691871 | 2 |
| #20263929 | 2 |
| #20263876 | 2 |
| C22⋊(C199⋊C8) | 2 |
| C22×D4×C199 | 2 |
| #447 | 199 |