Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×(C2×D199)⋊C4 | C2 | semidirect |
| 3. C2×C4×Dic199 | C2 | semidirect |
| 4. C2×C4⋊C4×C199 | C2 | semidirect |
| 8. C2×D796 | C4 | semidirect |
| 23. C2×Dic199 | D4 | semidirect |
| 41. C4×C199 | C22⋊C4 | semidirect |
| 49. C199 | #390 | semidirect |
| 52. C2×C4⋊C4 | D199 | semidirect |
| 92. C4 | (C2×D199)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D796 | 2 |
| C2×(C2×D199)⋊C4 | 2 |
| C2×C4×Dic199 | 2 |
| C2×C4⋊C4×C199 | 2 |
| #390 | 199 |