Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
332 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 332 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. C2×#16812117 | C2 | semidirect |
| 3. #20292626 | C2 | semidirect |
| 4. C2×#16812029 | C2 | semidirect |
| 5. C2×#16812025 | C2 | semidirect |
| 6. #20292391 | C2 | semidirect |
| 7. #343×C107 | C2 | semidirect |
| 11. #16812137 | C4 | semidirect |
| 124. C107 | #1907 | semidirect |
| 130. #343 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812137 | 2 |
| C2×#16812117 | 2 |
| #20292626 | 2 |
| C2×#16812029 | 2 |
| C2×#16812025 | 2 |
| #20292391 | 2 |
| #343×C107 | 2 |
| #1907 | 107 |