Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
316 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#16812043 | C2 | semidirect |
| 3. C2×#16812041 | C2 | semidirect |
| 5. #20292390 | C2 | semidirect |
| 6. #20292390 | C2 | semidirect |
| 23. C22⋊C8×C107 | C4 | semidirect |
| 121. C107 | #1854 | semidirect |
| 143. C22⋊C8 | Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812068 | 2 |
| C2×#16812043 | 2 |
| C2×#16812041 | 2 |
| #20292487 | 2 |
| #20292390 | 2 |
| C2×C22⋊C8×C107 | 2 |
| #1854 | 107 |