Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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. #20263980 | C2 | semidirect |
| 2. C2×#15691871 | C2 | semidirect |
| 3. #20263962 | C2 | semidirect |
| 4. #20263890 | C2 | semidirect |
| 5. #20263872 | C2 | semidirect |
| 6. #20263871 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C199 | C2 | semidirect |
| 53. C199 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263980 | 2 |
| C2×#15691871 | 2 |
| #20263962 | 2 |
| #20263890 | 2 |
| #20263872 | 2 |
| #20263871 | 2 |
| AGL(1,ℤ/8)×C199 | 2 |
| #472 | 199 |