Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20292644 | C2 | semidirect |
| 3. #20292633 | C2 | semidirect |
| 4. C2×#16812025 | C2 | semidirect |
| 5. #20292399 | C2 | semidirect |
| 6. C107⋊#338 | C2 | semidirect |
| 7. #568×C107 | C2 | semidirect |
| 11. C2×#13133805 | C4 | semidirect |
| 12. C2×#13133803 | C4 | semidirect |
| 113. C107 | #1903 | semidirect |
| 115. #568 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812134 | 2 |
| #20292644 | 2 |
| #20292633 | 2 |
| C2×#16812025 | 2 |
| #20292399 | 2 |
| C107⋊#338 | 2 |
| #568×C107 | 2 |
| #1903 | 107 |