Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13133808 | C2 | semidirect |
| 3. C2×C4×Dic214 | C2 | semidirect |
| 4. #20292846 | C2 | direct (N × H) |
| 5. C2×C4⋊(C107⋊C8) | C2 | semidirect |
| 6. C2×#16812033 | C2 | semidirect |
| 11. C2×#13133808 | C22 | semidirect |
| 17. C4×Dic214 | C22 | semidirect |
| 21. C4⋊(C107⋊C8) | C22 | semidirect |
| 22. #16812033 | C22 | semidirect |
| 111. C2×C107 | #464 | semidirect |
| 116. C107 | C2×#464 | semidirect |
| 227. C2 | #20292846 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133808 | 2 |
| C22×#13133806 | 2 |
| C2×C4×Dic214 | 2 |
| #20292846 | 2 |
| C2×C4⋊(C107⋊C8) | 2 |
| C2×#16812033 | 2 |
| C2×#16812030 | 2 |
| C2×#124×C107 | 2 |
| C2×#464 | 107 |