Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
188 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 47 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×#15691873 | C2 | semidirect |
| 3. #20263875 | C2 | semidirect |
| 4. C22⋊(C199⋊C8) | C2 | semidirect |
| 5. C22⋊Q8×C199 | C2 | semidirect |
| 11. C2×C199⋊C8 | C22 | semidirect |
| 12. C2×Q8×C199 | C22 | semidirect |
| 15. C4⋊C4×C199 | C22 | semidirect |
| 34. C22×C199 | SD16 | semidirect |
| 49. C199 | #450 | semidirect |
| 53. C22⋊Q8 | D199 | semidirect |
| 57. C2×Q8 | C2×D199 | semidirect |
| 65. C4⋊C4 | C2×D199 | semidirect |
| 88. C22 | #15691873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D796 | 2 |
| C2×#15691873 | 2 |
| #20263875 | 2 |
| C22⋊(C199⋊C8) | 2 |
| C22⋊Q8×C199 | 2 |
| #450 | 199 |