Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
304 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 77 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. C4×C22⋊Dic107 | C2 | semidirect |
| 3. #20292365 | C2 | semidirect |
| 4. #20292362 | C2 | semidirect |
| 5. C2×C22⋊C8×C107 | C2 | semidirect |
| 6. C2×#13133818 | C4 | semidirect |
| 8. #16812088 | C4 | semidirect |
| 10. #16812083 | C4 | semidirect |
| 15. #16812068 | C4 | semidirect |
| 113. C107 | #1501 | semidirect |
| 115. C2×C22⋊C8 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293138 | 2 |
| C4×C22⋊Dic107 | 2 |
| #20292365 | 2 |
| #20292362 | 2 |
| C2×C22⋊C8×C107 | 2 |
| #1501 | 107 |