Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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. Q8×Dic199 | C2 | semidirect |
| 4. #20263888 | C2 | semidirect |
| 6. #20263865 | C2 | semidirect |
| 7. #103×C199 | C2 | semidirect |
| 10. #15691873 | C4 | semidirect |
| 27. C199⋊C8 | C2×C4 | semidirect |
| 29. Q8×C199 | C2×C4 | semidirect |
| 49. C199 | #440 | semidirect |
| 55. #103 | D199 | semidirect |
| 72. Q8 | C4×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691873 | 2 |
| Q8×Dic199 | 2 |
| #20263917 | 2 |
| #20263888 | 2 |
| #20263877 | 2 |
| #20263865 | 2 |
| #103×C199 | 2 |
| #440 | 199 |