Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. C4⋊C4×Dic107 | C2 | semidirect |
| 5. #20292389 | C2 | semidirect |
| 6. #20292381 | C2 | semidirect |
| 7. C2×#106×C107 | C2 | semidirect |
| 15. #16812031 | C4 | semidirect |
| 119. C107 | #1926 | semidirect |
| 120. C2×#106 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812031 | 2 |
| C2×#16812029 | 2 |
| #20292528 | 2 |
| C4⋊C4×Dic107 | 2 |
| #20292389 | 2 |
| #20292381 | 2 |
| C2×#106×C107 | 2 |
| #1926 | 107 |