Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
674 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 674 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 |
|---|---|---|
| 2. C22×C4×D199 | C2 | semidirect |
| 3. C2×C22⋊Dic199 | C2 | semidirect |
| 4. C2×(C2×D199)⋊C4 | C2 | semidirect |
| 5. C22⋊C4×D199 | C2 | direct (N × H) |
| 6. C2×C22⋊C4×C199 | C2 | semidirect |
| 8. C23×D199 | C4 | semidirect |
| 12. C22×Dic199 | C22 | semidirect |
| 14. C2×C4×D199 | C22 | semidirect |
| 15. C22⋊Dic199 | C22 | semidirect |
| 16. (C2×D199)⋊C4 | C22 | semidirect |
| 18. C22×C4×C199 | C22 | semidirect |
| 19. C22⋊C4×C199 | C22 | semidirect |
| 24. C22×D199 | C2×C4 | semidirect |
| 25. C22×D199 | C2×C4 | semidirect |
| 30. C2×Dic199 | C23 | semidirect |
| 33. C23×C199 | C2×C4 | semidirect |
| 37. C2×C4×C199 | C23 | semidirect |
| 41. C22×C199 | C22×C4 | semidirect |
| 47. C2×D199 | C22⋊C4 | direct (N × H) |
| 49. C2×D199 | C22×C4 | semidirect |
| 54. C2×C199 | C2×C22⋊C4 | semidirect |
| 58. D199 | C2×C22⋊C4 | direct (N × H) |
| 59. C199 | C22×C22⋊C4 | semidirect |
| 66. C2×C22⋊C4 | D199 | direct (N × H) |
| 76. C22×C4 | C2×D199 | semidirect |
| 79. C22⋊C4 | C2×D199 | direct (N × H) |
| 90. C23 | C4×D199 | semidirect |
| 97. C2×C4 | C22×D199 | semidirect |
| 108. C22 | C2×C4×D199 | semidirect |
| 116. C2 | C22⋊C4×D199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D199 | 2 |
| C22×C4×D199 | 2 |
| C2×C22⋊Dic199 | 2 |
| C2×(C2×D199)⋊C4 | 2 |
| C22⋊C4×D199 | 2 |
| C2×C22⋊C4×C199 | 2 |
| C22×C22⋊C4 | 199 |