Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 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⋊C4×D199 | C2 | semidirect |
| 3. #20263870 | C2 | semidirect |
| 4. #20263869 | C2 | semidirect |
| 5. #99×C199 | C2 | semidirect |
| 6. C23×D199 | C4 | semidirect |
| 8. C2×D796 | C4 | semidirect |
| 9. C2×C22⋊D199 | C4 | semidirect |
| 14. C2×C4×D199 | C4 | semidirect |
| 15. C22⋊Dic199 | C22 | semidirect |
| 18. C22⋊C4×C199 | C22 | semidirect |
| 25. C22×D199 | C2×C4 | semidirect |
| 32. C2×Dic199 | C2×C4 | semidirect |
| 36. C23×C199 | C2×C4 | semidirect |
| 40. C2×C4×C199 | C2×C4 | semidirect |
| 68. D199 | #99 | direct (N × H) |
| 69. C199 | C2×#99 | semidirect |
| 75. #99 | D199 | direct (N × H) |
| 88. C22⋊C4 | C2×D199 | semidirect |
| 98. C23 | C4×D199 | semidirect |
| 110. C2×C4 | C4×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D199 | 2 |
| C22⋊C4×D199 | 2 |
| #20263870 | 2 |
| #20263869 | 2 |
| #99×C199 | 2 |
| C2×#99 | 199 |