Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
242 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20263935 | C2 | semidirect |
| 2. #20263934 | C2 | semidirect |
| 3. #20263933 | C2 | semidirect |
| 4. #20263933 | C2 | semidirect |
| 5. #20263932 | C2 | semidirect |
| 6. #20263931 | C2 | semidirect |
| 9. C22⋊Q8×C199 | C2 | semidirect |
| 11. C2×Dic398 | C22 | semidirect |
| 12. C2×Dic398 | C22 | semidirect |
| 16. C4⋊Dic199 | C22 | semidirect |
| 17. C4⋊Dic199 | C22 | semidirect |
| 18. Dic199⋊C4 | C22 | semidirect |
| 19. Dic199⋊C4 | C22 | semidirect |
| 20. Dic199⋊C4 | C22 | semidirect |
| 26. C2×Q8×C199 | C22 | semidirect |
| 28. C4⋊C4×C199 | C22 | semidirect |
| 29. C4⋊C4×C199 | C22 | semidirect |
| 33. C22×D199 | Q8 | semidirect |
| 70. C199 | #543 | semidirect |
| 78. C22⋊Q8 | D199 | semidirect |
| 84. C2×Q8 | C2×D199 | semidirect |
| 94. C4⋊C4 | C2×D199 | semidirect |
| 95. C4⋊C4 | C2×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263935 | 2 |
| #20263934 | 2 |
| #20263933 | 2 |
| #20263932 | 2 |
| #20263931 | 2 |
| C2×(C2×D199)⋊C4 | 2 |
| C22⋊C4×D199 | 2 |
| C22⋊Q8×C199 | 2 |
| #543 | 199 |