Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
348 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 107 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×#16812040 | C2 | semidirect |
| 3. C2×#16812032 | C2 | semidirect |
| 5. C2×C4×C107⋊C8 | C2 | semidirect |
| 6. #20292533 | C2 | semidirect |
| 11. C2×#13133806 | C4 | semidirect |
| 70. C2×C4×C107 | SD16 | semidirect |
| 87. C107⋊C8 | C22⋊C4 | semidirect |
| 113. C107 | #1968 | semidirect |
| 192. C2×C4 | #13133806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133806 | 2 |
| C2×#16812040 | 2 |
| C2×#16812032 | 2 |
| C2×#16812030 | 2 |
| C2×C4×C107⋊C8 | 2 |
| #20292533 | 2 |
| #390×C107 | 2 |
| #1968 | 107 |