Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#15691876 | C2 | semidirect |
| 3. C2×#15691873 | C2 | semidirect |
| 4. #20263878 | C2 | semidirect |
| 5. #20263875 | C2 | semidirect |
| 6. C22⋊(C199⋊C8) | C2 | semidirect |
| 7. C22⋊Q8×C199 | C2 | semidirect |
| 60. C199 | #452 | semidirect |
| 65. C22⋊Q8 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691886 | 2 |
| C2×#15691876 | 2 |
| C2×#15691873 | 2 |
| #20263878 | 2 |
| #20263875 | 2 |
| C22⋊(C199⋊C8) | 2 |
| C22⋊Q8×C199 | 2 |
| #452 | 199 |