Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
426 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 175 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. C22×C4×D199 | C2 | semidirect |
| 4. (C22⋊D199)⋊C4 | C2 | direct (N × H) |
| 5. C2×Dic199⋊C4 | C2 | semidirect |
| 6. C2×(C2×D199)⋊C4 | C2 | semidirect |
| 7. C2×C4×Dic199 | C2 | semidirect |
| 8. C2×C22⋊C4×C199 | C2 | semidirect |
| 10. C2×C22⋊D199 | C4 | semidirect |
| 16. C22×Dic199 | C22 | semidirect |
| 18. C2×C4×D199 | C22 | semidirect |
| 19. Dic199⋊C4 | C22 | semidirect |
| 20. (C2×D199)⋊C4 | C22 | semidirect |
| 21. C4×Dic199 | C22 | semidirect |
| 25. C22⋊C4×C199 | C22 | semidirect |
| 28. C22×D199 | C2×C4 | semidirect |
| 30. C22⋊D199 | C2×C4 | semidirect |
| 33. C2×Dic199 | C2×C4 | semidirect |
| 34. C2×Dic199 | D4 | semidirect |
| 41. C23×C199 | C2×C4 | semidirect |
| 52. C22×C199 | C22×C4 | semidirect |
| 59. C2×D199 | C22×C4 | semidirect |
| 63. Dic199 | C22×C4 | semidirect |
| 64. Dic199 | C2×D4 | semidirect |
| 66. C2×C199 | C4×D4 | semidirect |
| 71. C199 | C2×C4×D4 | semidirect |
| 79. C2×C22⋊C4 | D199 | semidirect |
| 96. C22⋊C4 | C2×D199 | semidirect |
| 104. C23 | C4×D199 | semidirect |
| 128. C22 | C2×C4×D199 | semidirect |
| 139. C2 | (C22⋊D199)⋊C4 | 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 |
| C22×C4×D199 | 2 |
| (C22⋊D199)⋊C4 | 2 |
| C2×Dic199⋊C4 | 2 |
| C2×(C2×D199)⋊C4 | 2 |
| C2×C4×Dic199 | 2 |
| C2×C22⋊C4×C199 | 2 |
| C2×C4×D4 | 199 |