Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
232 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #20292430 | C2 | direct (N × H) |
| 8. C2×Dic428 | C4 | semidirect |
| 23. Dic428 | C2×C4 | semidirect |
| 57. C2×C107 | #358 | semidirect |
| 62. C107 | C2×#358 | semidirect |
| 119. C2 | #20292430 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic428 | 2 |
| C22×C107⋊C16 | 2 |
| #20292430 | 2 |
| C2×#107×C107 | 2 |
| C2×#358 | 107 |