Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
166 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 49 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. #20293005 | C2 | semidirect |
| 5. Dic107⋊C16 | C2 | semidirect |
| 6. #20292430 | C2 | semidirect |
| 7. #358×C107 | C2 | semidirect |
| 68. Dic107 | SD32 | semidirect |
| 74. C107 | #2208 | semidirect |
| 81. #358 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812054 | 2 |
| C2×#16812052 | 2 |
| #20293005 | 2 |
| #20292709 | 2 |
| Dic107⋊C16 | 2 |
| #20292430 | 2 |
| #358×C107 | 2 |
| #2208 | 107 |