Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×Dic428 | C2 | semidirect |
| 4. C2×#16812074 | C2 | semidirect |
| 5. #20292848 | C2 | direct (N × H) |
| 6. C2×Dic107⋊C8 | C2 | semidirect |
| 7. C2×#16812032 | C2 | semidirect |
| 12. C2×Dic428 | C22 | semidirect |
| 19. #16812074 | C22 | semidirect |
| 25. Dic107⋊C8 | C22 | semidirect |
| 26. #16812032 | C22 | semidirect |
| 111. C2×C107 | #464 | semidirect |
| 116. C107 | C2×#464 | semidirect |
| 227. C2 | #20292848 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic428 | 2 |
| C22×#13133806 | 2 |
| C2×#16812096 | 2 |
| C2×#16812074 | 2 |
| #20292848 | 2 |
| C2×Dic107⋊C8 | 2 |
| C2×#16812032 | 2 |
| C2×#102×C107 | 2 |
| C2×#464 | 107 |