Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
330 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 159 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. #20263914 | C2 | semidirect |
| 3. #20263913 | C2 | semidirect |
| 4. #20263912 | C2 | semidirect |
| 5. #20263911 | C2 | semidirect |
| 6. C4⋊C4×D199 | C2 | semidirect |
| 8. C42×D199 | C2 | semidirect |
| 9. #117×C199 | C2 | semidirect |
| 12. C2×C4×D199 | C4 | semidirect |
| 18. C4⋊Dic199 | C22 | semidirect |
| 19. Dic199⋊C4 | C22 | semidirect |
| 22. C4×Dic199 | C22 | semidirect |
| 23. C4×Dic199 | C22 | semidirect |
| 25. C4⋊C4×C199 | C22 | semidirect |
| 27. C42×C199 | C22 | semidirect |
| 32. C2×Dic199 | C2×C4 | semidirect |
| 39. C4×D199 | C2×C4 | semidirect |
| 40. C4×D199 | C2×C4 | semidirect |
| 42. C2×C4×C199 | C2×C4 | semidirect |
| 64. D199 | #117 | direct (N × H) |
| 65. C199 | C2×#117 | semidirect |
| 72. #117 | D199 | direct (N × H) |
| 87. C4⋊C4 | C2×D199 | semidirect |
| 93. C42 | C2×D199 | semidirect |
| 108. C2×C4 | C4×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D199 | 2 |
| #20263914 | 2 |
| #20263913 | 2 |
| #20263912 | 2 |
| #20263911 | 2 |
| C4⋊C4×D199 | 2 |
| C22⋊C4×D199 | 2 |
| C42×D199 | 2 |
| #117×C199 | 2 |
| C2×#117 | 199 |