Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #20292650 | C2 | semidirect |
| 3. C2×#16812027 | C2 | semidirect |
| 4. C2×#16812027 | C2 | semidirect |
| 6. M16×Dic107 | C2 | semidirect |
| 109. C107 | #1967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812096 | 2 |
| #20292650 | 2 |
| C2×#16812027 | 2 |
| C2×#16812026 | 2 |
| M16×Dic107 | 2 |
| C2×#100×C107 | 2 |
| #1967 | 107 |