Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
326 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20292667 | C2 | semidirect |
| 3. C2×#16812037 | C2 | semidirect |
| 4. #20292626 | C2 | semidirect |
| 5. C2×#16812026 | C2 | semidirect |
| 6. #20292387 | C2 | semidirect |
| 7. #390×C107 | C2 | semidirect |
| 40. #13133802 | D4 | semidirect |
| 131. C107 | #2037 | semidirect |
| 137. #390 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293194 | 2 |
| #20292667 | 2 |
| C2×#16812037 | 2 |
| #20292626 | 2 |
| C2×#16812026 | 2 |
| #20292387 | 2 |
| #390×C107 | 2 |
| #2037 | 107 |