Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
156 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 156 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 |
|---|---|---|
| 3. #20292455 | C2 | semidirect |
| 4. #20292453 | C2 | semidirect |
| 14. M32×C107 | C4 | semidirect |
| 28. C16×C107 | C2×C4 | semidirect |
| 56. C107 | #2159 | semidirect |
| 65. M32 | Dic107 | semidirect |
| 84. C16 | C2×Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292665 | 2 |
| C2×#16812043 | 2 |
| #20292455 | 2 |
| #20292453 | 2 |
| C2×M32×C107 | 2 |
| #2159 | 107 |