Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20263869 | C2 | semidirect |
| 4. #117×C199 | C2 | semidirect |
| 9. C2×Dic398 | C4 | semidirect |
| 10. C2×D796 | C4 | semidirect |
| 12. C2×C4×D199 | C4 | semidirect |
| 57. C199 | #410 | semidirect |
| 61. #117 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691886 | 2 |
| #20263914 | 2 |
| #20263869 | 2 |
| #117×C199 | 2 |
| #410 | 199 |