Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
418 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 3. C2×C4⋊Dic199 | C2 | semidirect |
| 4. C2×Dic199⋊C4 | C2 | semidirect |
| 5. C4⋊C4×D199 | C2 | direct (N × H) |
| 6. C2×C4⋊C4×C199 | C2 | semidirect |
| 11. C2×C4×D199 | C4 | semidirect |
| 14. C4⋊Dic199 | C22 | semidirect |
| 15. Dic199⋊C4 | C22 | semidirect |
| 18. C4⋊C4×C199 | C22 | semidirect |
| 24. C2×Dic199 | C2×C4 | semidirect |
| 28. C4×D199 | C2×C4 | semidirect |
| 31. C2×C4×C199 | C2×C4 | semidirect |
| 38. C2×D199 | C4⋊C4 | direct (N × H) |
| 43. C4×C199 | C22×C4 | semidirect |
| 45. Dic199 | C22×C4 | semidirect |
| 46. C2×C199 | C2×C4⋊C4 | semidirect |
| 50. D199 | C2×C4⋊C4 | direct (N × H) |
| 51. C199 | C22×C4⋊C4 | semidirect |
| 58. C2×C4⋊C4 | D199 | direct (N × H) |
| 70. C4⋊C4 | C2×D199 | direct (N × H) |
| 83. C2×C4 | C4×D199 | semidirect |
| 97. C4 | C2×C4×D199 | semidirect |
| 99. C2 | C4⋊C4×D199 | 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 |
| C2×C4⋊Dic199 | 2 |
| C2×Dic199⋊C4 | 2 |
| C4⋊C4×D199 | 2 |
| C2×C4⋊C4×C199 | 2 |
| C22×C4⋊C4 | 199 |