Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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×#16812109 | C2 | semidirect |
| 3. C2×#16812097 | C2 | semidirect |
| 4. C2×#16812088 | C2 | semidirect |
| 5. #20292543 | C2 | semidirect |
| 6. #20292533 | C2 | semidirect |
| 7. #20292529 | C2 | semidirect |
| 8. #20292501 | C2 | semidirect |
| 9. C4×C22⋊C4×C107 | C2 | semidirect |
| 93. C2×C4×C107 | #41 | semidirect |
| 137. C107 | #2432 | semidirect |
| 146. C4×C22⋊C4 | D107 | semidirect |
| 243. C2×C4 | #13133818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133818 | 2 |
| C2×#16812109 | 2 |
| C2×#16812097 | 2 |
| C2×#16812088 | 2 |
| #20292543 | 2 |
| #20292533 | 2 |
| #20292529 | 2 |
| #20292501 | 2 |
| C4×C22⋊C4×C107 | 2 |
| #2432 | 107 |