Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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×#16812035 | C2 | semidirect |
| 3. #20292626 | C2 | semidirect |
| 4. C2×#16812025 | C2 | semidirect |
| 5. #20292528 | C2 | semidirect |
| 6. #20292386 | C2 | semidirect |
| 7. #428×C107 | C2 | semidirect |
| 56. M16×C107 | D4 | semidirect |
| 131. C107 | #2037 | semidirect |
| 133. #428 | D107 | semidirect |
| 181. M16 | D428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293196 | 2 |
| C2×#16812035 | 2 |
| #20292626 | 2 |
| C2×#16812025 | 2 |
| #20292528 | 2 |
| #20292386 | 2 |
| #428×C107 | 2 |
| #2037 | 107 |