Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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. C22×C199⋊C8 | C2 | semidirect |
| 3. #20263929 | C2 | semidirect |
| 4. #20263888 | C2 | semidirect |
| 5. #20263876 | C2 | semidirect |
| 6. #20263875 | C2 | semidirect |
| 7. #121×C199 | C2 | semidirect |
| 27. C199⋊C8 | D4 | semidirect |
| 43. C22×C199 | D8 | semidirect |
| 59. C199 | #466 | semidirect |
| 64. #121 | D199 | semidirect |
| 106. 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 |
| C22×C199⋊C8 | 2 |
| #20263929 | 2 |
| #20263888 | 2 |
| #20263876 | 2 |
| #20263875 | 2 |
| #121×C199 | 2 |
| #466 | 199 |