Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 10. #16812055 | C4 | direct (N × H) |
| 55. C4×C107 | Q32 | semidirect |
| 64. C107 | C4×Q32 | semidirect |
| 121. C4 | #16812055 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812055 | 2 |
| C4×Dic428 | 2 |
| #20292452 | 2 |
| #20292431 | 2 |
| #20292430 | 2 |
| C4×C107⋊C16 | 2 |
| C4×Q16×C107 | 2 |
| C4×Q32 | 107 |