Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
246 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 246 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 |
|---|---|---|
| 1. #20263950 | C2 | direct (N × H) |
| 2. C2×C4⋊Dic199 | C2 | semidirect |
| 3. C2×Dic199⋊C4 | C2 | semidirect |
| 7. C2×C4×Dic199 | C2 | semidirect |
| 8. C2×C4⋊C4×C199 | C2 | semidirect |
| 13. C4⋊Dic199 | C22 | semidirect |
| 14. Dic199⋊C4 | C22 | semidirect |
| 18. C4×Dic199 | C22 | semidirect |
| 22. C4⋊C4×C199 | C22 | semidirect |
| 54. C2×C199 | #126 | semidirect |
| 59. C199 | C2×#126 | semidirect |
| 64. C2×C4⋊C4 | D199 | semidirect |
| 78. C4⋊C4 | C2×D199 | semidirect |
| 115. C2 | #20263950 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263950 | 2 |
| C2×C4⋊Dic199 | 2 |
| C2×Dic199⋊C4 | 2 |
| C2×(C2×D199)⋊C4 | 2 |
| C2×C4×Dic199 | 2 |
| C2×C4⋊C4×C199 | 2 |
| C2×#126 | 199 |