Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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×#16812052 | C2 | semidirect |
| 2. C2×D1712 | C2 | semidirect |
| 3. C2×#16812050 | C2 | semidirect |
| 4. #20293012 | C2 | semidirect |
| 5. #20293002 | C2 | semidirect |
| 6. #20292402 | C2 | semidirect |
| 7. C2×SD32×C107 | C2 | semidirect |
| 35. C107⋊C16 | D4 | semidirect |
| 43. C16×C107 | D4 | semidirect |
| 79. C107 | #2250 | semidirect |
| 81. C2×SD32 | D107 | semidirect |
| 122. C16 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812052 | 2 |
| C2×D1712 | 2 |
| C2×#16812050 | 2 |
| #20293012 | 2 |
| #20293002 | 2 |
| #20292402 | 2 |
| C2×SD32×C107 | 2 |
| #2250 | 107 |