Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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×Q8×D199 | C2 | semidirect |
| 3. #20263954 | C2 | semidirect |
| 4. #20263941 | C2 | semidirect |
| 5. #20263940 | C2 | semidirect |
| 6. #20263937 | C2 | semidirect |
| 7. #20263935 | C2 | semidirect |
| 8. #20263934 | C2 | semidirect |
| 9. #20263931 | C2 | semidirect |
| 10. #20263913 | C2 | semidirect |
| 11. C22⋊Q8×C199 | C2 | semidirect |
| 83. C199 | #536 | semidirect |
| 94. 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×Q8×D199 | 2 |
| #20263954 | 2 |
| #20263941 | 2 |
| #20263940 | 2 |
| #20263937 | 2 |
| #20263935 | 2 |
| #20263934 | 2 |
| #20263931 | 2 |
| #20263913 | 2 |
| C22⋊Q8×C199 | 2 |
| #536 | 199 |