Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
1008 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 309 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 |
|---|---|---|
| 1. C22×#13133802 | C2 | semidirect |
| 2. C2×#16812068 | C2 | semidirect |
| 3. #20292632 | C2 | direct (N × H) |
| 4. C2×#16812030 | C2 | semidirect |
| 7. C2×#13133802 | C22 | semidirect |
| 8. C22×C107⋊C8 | C22 | semidirect |
| 10. #16812068 | C22 | semidirect |
| 11. C2×C4⋊Dic107 | C22 | semidirect |
| 14. #16812030 | C22 | semidirect |
| 19. C22×D4×C107 | C4 | semidirect |
| 26. C2×C107⋊C8 | C23 | semidirect |
| 28. C4⋊Dic107 | C23 | semidirect |
| 43. C2×D4×C107 | C2×C4 | semidirect |
| 94. C2×C107 | #418 | semidirect |
| 98. C107 | C2×#418 | semidirect |
| 108. C22×D4 | Dic107 | semidirect |
| 133. C2×D4 | C2×Dic107 | semidirect |
| 192. C2 | #20292632 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133802 | 2 |
| C2×#16812068 | 2 |
| #20292632 | 2 |
| C2×#16812030 | 2 |
| C23×D4×C107 | 2 |
| C2×#418 | 107 |