Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
426 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 169 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. C4×D796 | C2 | semidirect |
| 4. D4×Dic199 | C2 | semidirect |
| 5. #20263917 | C2 | semidirect |
| 6. C4×C22⋊D199 | C2 | semidirect |
| 7. (C22⋊D199)⋊C4 | C2 | semidirect |
| 8. C4⋊C4×D199 | C2 | semidirect |
| 9. C22⋊C4×D199 | C2 | semidirect |
| 10. C42×D199 | C2 | semidirect |
| 11. C4×D4×C199 | C2 | semidirect |
| 15. D4×D199 | C4 | direct (N × H) |
| 16. C22×Dic199 | C22 | semidirect |
| 22. C2×C4×D199 | C22 | semidirect |
| 23. C2×C4×D199 | C22 | semidirect |
| 24. C4⋊Dic199 | C22 | semidirect |
| 25. Dic199⋊C4 | C22 | semidirect |
| 26. C22⋊Dic199 | C22 | semidirect |
| 27. (C2×D199)⋊C4 | C22 | semidirect |
| 28. (C2×D199)⋊C4 | C22 | semidirect |
| 29. C4×Dic199 | C22 | semidirect |
| 30. C4×Dic199 | C22 | semidirect |
| 31. C4×Dic199 | C22 | semidirect |
| 33. C22×C4×C199 | C22 | semidirect |
| 34. C4⋊C4×C199 | C22 | semidirect |
| 35. C22⋊C4×C199 | C22 | semidirect |
| 36. C42×C199 | C22 | semidirect |
| 39. C22×D199 | C2×C4 | semidirect |
| 42. D796 | C2×C4 | semidirect |
| 43. C22⋊D199 | C2×C4 | semidirect |
| 53. C4×D199 | C2×C4 | semidirect |
| 54. C4×D199 | D4 | direct (N × H) |
| 56. D4×C199 | C2×C4 | semidirect |
| 64. C22×C199 | C22×C4 | semidirect |
| 70. C2×D199 | C22×C4 | semidirect |
| 75. C4×C199 | C22×C4 | semidirect |
| 76. C4×C199 | C2×D4 | semidirect |
| 79. Dic199 | C22×C4 | semidirect |
| 80. Dic199 | C2×D4 | semidirect |
| 86. D199 | C4×D4 | direct (N × H) |
| 87. C199 | C2×C4×D4 | semidirect |
| 96. C4×D4 | D199 | direct (N × H) |
| 113. C22×C4 | C2×D199 | semidirect |
| 116. C4⋊C4 | C2×D199 | semidirect |
| 120. C22⋊C4 | C2×D199 | semidirect |
| 124. C42 | C2×D199 | semidirect |
| 133. D4 | C4×D199 | direct (N × H) |
| 159. C22 | C2×C4×D199 | semidirect |
| 167. C4 | C2×C4×D199 | semidirect |
| 168. C4 | D4×D199 | direct (N × H) |
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 |
| C4×D796 | 2 |
| D4×Dic199 | 2 |
| #20263917 | 2 |
| C4×C22⋊D199 | 2 |
| (C22⋊D199)⋊C4 | 2 |
| C4⋊C4×D199 | 2 |
| C22⋊C4×D199 | 2 |
| C42×D199 | 2 |
| C4×D4×C199 | 2 |
| C2×C4×D4 | 199 |