Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
406 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#16812107 | C2 | semidirect |
| 3. C2×#16812034 | C2 | semidirect |
| 4. C2×#16812033 | C2 | semidirect |
| 6. #20292381 | C2 | semidirect |
| 95. C2×Dic107 | SD16 | semidirect |
| 127. C107 | #2013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133806 | 2 |
| C2×#16812107 | 2 |
| C2×#16812034 | 2 |
| C2×#16812033 | 2 |
| #20292530 | 2 |
| #20292381 | 2 |
| C22×SD16×C107 | 2 |
| #2013 | 107 |