Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
284 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 3. #20292421 | C2 | direct (N × H) |
| 5. C22×Dic214 | C4 | semidirect |
| 8. #16812096 | C4 | semidirect |
| 13. C2×C4×Dic107 | C4 | semidirect |
| 23. C2×Dic214 | C2×C4 | semidirect |
| 34. C4×Dic107 | C2×C4 | semidirect |
| 105. C2×C107 | #354 | semidirect |
| 108. C107 | C2×#354 | semidirect |
| 213. C2 | #20292421 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812096 | 2 |
| C2×#16812024 | 2 |
| #20292421 | 2 |
| C2×#99×C107 | 2 |
| C2×#354 | 107 |