Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 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. C22×C199⋊C8 | C2 | semidirect |
| 3. (C2×D199)⋊C8 | C2 | direct (N × H) |
| 4. C22×C8×C199 | C2 | semidirect |
| 12. C2×C199⋊C8 | C22 | semidirect |
| 15. C2×C8×C199 | C22 | semidirect |
| 18. C22×D199 | C8 | semidirect |
| 39. C2×D199 | C2×C8 | semidirect |
| 44. C2×C199 | C22⋊C8 | semidirect |
| 49. C199 | C2×C22⋊C8 | semidirect |
| 53. C22×C8 | D199 | semidirect |
| 65. C2×C8 | C2×D199 | semidirect |
| 95. C2 | (C2×D199)⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D199 | 2 |
| C22×C199⋊C8 | 2 |
| (C2×D199)⋊C8 | 2 |
| C22×C8×C199 | 2 |
| C2×C22⋊C8 | 199 |