Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. C2×#16812055 | C2 | semidirect |
| 4. #20292452 | C2 | semidirect |
| 5. #20292431 | C2 | semidirect |
| 6. #20292430 | C2 | semidirect |
| 58. C22×C107 | Q32 | semidirect |
| 72. C107 | #2216 | semidirect |
| 130. C22 | #16812055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812055 | 2 |
| C22×C107⋊C16 | 2 |
| #20292868 | 2 |
| #20292452 | 2 |
| #20292431 | 2 |
| #20292430 | 2 |
| #467×C107 | 2 |
| #2216 | 107 |