Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
506 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 95 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×C22⋊Dic199 | C2 | semidirect |
| 3. C2×(C2×D199)⋊C4 | C2 | semidirect |
| 4. C2×C22⋊C4×C199 | C2 | semidirect |
| 8. C23×D199 | C4 | semidirect |
| 10. C22×Dic199 | C22 | semidirect |
| 14. C22×C4×C199 | C22 | semidirect |
| 37. C22×C199 | C22⋊C4 | semidirect |
| 47. C2×D199 | C22⋊C4 | semidirect |
| 56. C199 | #379 | semidirect |
| 61. C2×C22⋊C4 | D199 | semidirect |
| 69. C22×C4 | C2×D199 | semidirect |
| 100. C22 | (C2×D199)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D199 | 2 |
| C2×C22⋊Dic199 | 2 |
| C2×(C2×D199)⋊C4 | 2 |
| C2×C22⋊C4×C199 | 2 |
| #379 | 199 |