Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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×C4×Dic199 | C2 | semidirect |
| 3. #20263881 | C2 | direct (N × H) |
| 4. C2×M16×C199 | C2 | semidirect |
| 7. #15691886 | C4 | semidirect |
| 9. C2×Dic398 | C4 | semidirect |
| 10. C2×D796 | C4 | semidirect |
| 15. C4×Dic199 | C22 | semidirect |
| 18. M16×C199 | C22 | semidirect |
| 22. Dic398 | C2×C4 | semidirect |
| 24. D796 | C2×C4 | semidirect |
| 54. C2×C199 | #104 | semidirect |
| 57. C199 | C2×#104 | semidirect |
| 60. C2×M16 | D199 | semidirect |
| 74. M16 | C2×D199 | semidirect |
| 113. C2 | #20263881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691886 | 2 |
| C2×C4×Dic199 | 2 |
| #20263881 | 2 |
| C2×M16×C199 | 2 |
| C2×#104 | 199 |