Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
628 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 325 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 |
|---|---|---|
| 10. C4×Dic214 | C4 | semidirect |
| 11. #16812074 | C4 | semidirect |
| 69. Dic214 | C42 | semidirect |
| 89. C107 | #2276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic214 | 2 |
| C2×#16812074 | 2 |
| C4⋊C4×Dic107 | 2 |
| C4×Dic107⋊C4 | 2 |
| #20292478 | 2 |
| #20292473 | 2 |
| #20292472 | 2 |
| C4×C4⋊C4×C107 | 2 |
| #2276 | 107 |