Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
342 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 127 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. C23×Dic199 | C2 | semidirect |
| 3. #20263939 | C2 | direct (N × H) |
| 4. C2×C4⋊Dic199 | C2 | semidirect |
| 5. C2×(C2×D199)⋊C4 | C2 | semidirect |
| 6. C2×C22⋊C4×C199 | C2 | semidirect |
| 13. C22×Dic199 | C22 | semidirect |
| 14. C4⋊Dic199 | C22 | semidirect |
| 15. (C2×D199)⋊C4 | C22 | semidirect |
| 18. C22⋊C4×C199 | C22 | semidirect |
| 47. C2×C199 | #123 | semidirect |
| 51. C199 | C2×#123 | semidirect |
| 58. C2×C22⋊C4 | D199 | semidirect |
| 70. C22⋊C4 | C2×D199 | semidirect |
| 100. C2 | #20263939 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D199 | 2 |
| C23×Dic199 | 2 |
| #20263939 | 2 |
| C2×C4⋊Dic199 | 2 |
| C2×(C2×D199)⋊C4 | 2 |
| C2×C22⋊C4×C199 | 2 |
| C2×#123 | 199 |