Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
662 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. C24×D199 | C2 | semidirect |
| 2. C22×D796 | C2 | semidirect |
| 3. C22×C22⋊D199 | C2 | semidirect |
| 4. #20263925 | C2 | direct (N × H) |
| 5. C2×(C2×D199)⋊C4 | C2 | semidirect |
| 6. C2×C22⋊C4×C199 | C2 | semidirect |
| 10. C23×D199 | C22 | semidirect |
| 11. C23×D199 | C22 | semidirect |
| 13. C2×D796 | C22 | semidirect |
| 15. C2×C22⋊D199 | C22 | semidirect |
| 16. C22×Dic199 | C22 | semidirect |
| 17. (C2×D199)⋊C4 | C22 | semidirect |
| 19. C22×C4×C199 | C22 | semidirect |
| 20. C22⋊C4×C199 | C22 | semidirect |
| 28. C22×D199 | D4 | semidirect |
| 30. C22×D199 | C23 | semidirect |
| 34. C2×Dic199 | C23 | semidirect |
| 36. C23×C199 | D4 | semidirect |
| 40. C2×C4×C199 | C23 | semidirect |
| 45. C22×C199 | C2×D4 | semidirect |
| 54. C2×D199 | C2×D4 | semidirect |
| 58. C2×C199 | #120 | semidirect |
| 63. C199 | C2×#120 | semidirect |
| 70. C2×C22⋊C4 | D199 | semidirect |
| 82. C22×C4 | C2×D199 | semidirect |
| 84. C22⋊C4 | C2×D199 | semidirect |
| 96. C23 | D796 | semidirect |
| 104. C2×C4 | C22×D199 | semidirect |
| 117. C22 | C2×D796 | semidirect |
| 124. C2 | #20263925 | 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×D796 | 2 |
| C22×C22⋊D199 | 2 |
| #20263925 | 2 |
| C2×(C2×D199)⋊C4 | 2 |
| C2×C22⋊C4×C199 | 2 |
| C2×#120 | 199 |