Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 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 |
|---|---|---|
| 3. C2×C4×Dic199 | C2 | semidirect |
| 4. C199⋊#95 | C2 | semidirect |
| 7. C22×Dic199 | C4 | semidirect |
| 11. C22⋊Dic199 | C4 | semidirect |
| 15. C22⋊C4×C199 | C4 | semidirect |
| 22. C2×Dic199 | C2×C4 | semidirect |
| 32. C2×C4×C199 | C2×C4 | semidirect |
| 37. C22×C199 | C42 | semidirect |
| 46. Dic199 | C22⋊C4 | direct (N × H) |
| 53. C199 | C4×C22⋊C4 | semidirect |
| 68. C22⋊C4 | Dic199 | direct (N × H) |
| 86. C2×C4 | C2×Dic199 | semidirect |
| 91. C22 | C4×Dic199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic199 | 2 |
| C2×C22⋊Dic199 | 2 |
| C2×C4×Dic199 | 2 |
| C199⋊#95 | 2 |
| C2×C22⋊C4×C199 | 2 |
| C4×C22⋊C4 | 199 |