Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
484 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C2×#16812131 | C2 | semidirect |
| 2. #20293205 | C2 | semidirect |
| 3. #20292873 | C2 | semidirect |
| 4. #20292868 | C2 | semidirect |
| 5. #20292863 | C2 | semidirect |
| 6. C2×#16812043 | C2 | semidirect |
| 7. #20292629 | C2 | semidirect |
| 8. C2×#131×C107 | C2 | semidirect |
| 56. C2×C8×C107 | D4 | semidirect |
| 109. C107 | #3061 | semidirect |
| 111. C2×#131 | D107 | semidirect |
| 160. C2×C8 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| #20293205 | 2 |
| #20292873 | 2 |
| #20292868 | 2 |
| #20292863 | 2 |
| C2×#16812043 | 2 |
| #20292629 | 2 |
| C2×#131×C107 | 2 |
| #3061 | 107 |