Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
248 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 13. #16812034 | C4 | semidirect |
| 106. C107 | #1935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812034 | 2 |
| C2×#16812032 | 2 |
| C2×#16812019 | 2 |
| #20292532 | 2 |
| #20292523 | 2 |
| #20292389 | 2 |
| #340×C107 | 2 |
| #1935 | 107 |