Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
310 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 159 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. C4×Dic398 | C2 | semidirect |
| 3. C4×D796 | C2 | semidirect |
| 4. C4×C22⋊D199 | C2 | semidirect |
| 5. #20263914 | C2 | semidirect |
| 6. #20263912 | C2 | semidirect |
| 7. C42×D199 | C2 | semidirect |
| 8. C2×C42×C199 | C2 | semidirect |
| 9. #15691886 | C4 | direct (N × H) |
| 27. Dic398 | C2×C4 | semidirect |
| 28. D796 | C2×C4 | semidirect |
| 29. C22⋊D199 | C2×C4 | semidirect |
| 33. C4×D199 | C2×C4 | semidirect |
| 36. C2×C4×C199 | C2×C4 | semidirect |
| 49. C4×C199 | #41 | semidirect |
| 56. C199 | C4×#41 | semidirect |
| 65. C2×C42 | D199 | semidirect |
| 93. C2×C4 | C4×D199 | semidirect |
| 108. C4 | #15691886 | 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 |
| C4×Dic398 | 2 |
| C4×D796 | 2 |
| C4×C22⋊D199 | 2 |
| #20263914 | 2 |
| #20263912 | 2 |
| C42×D199 | 2 |
| C2×C42×C199 | 2 |
| C4×#41 | 199 |