Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
|---|---|---|
| 3. Q8×Dic199 | C2 | semidirect |
| 4. Dic199⋊C8 | C2 | semidirect |
| 5. #20263879 | C2 | semidirect |
| 7. C2×Q16×C199 | C2 | semidirect |
| 51. C199 | #464 | semidirect |
| 53. C2×Q16 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691873 | 2 |
| #20263944 | 2 |
| Q8×Dic199 | 2 |
| Dic199⋊C8 | 2 |
| #20263879 | 2 |
| #20263877 | 2 |
| C2×Q16×C199 | 2 |
| #464 | 199 |