Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 5. #16812109 | C4 | semidirect |
| 6. #16812109 | C4 | semidirect |
| 7. #16812101 | C4 | semidirect |
| 37. M16×C107 | Q8 | semidirect |
| 82. C107 | #1986 | semidirect |
| 109. M16 | Dic214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293184 | 2 |
| C4×C4⋊Dic107 | 2 |
| #20292388 | 2 |
| C4×M16×C107 | 2 |
| #1986 | 107 |