Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20293177 | C2 | semidirect |
| 2. #20293030 | C2 | semidirect |
| 3. #20293003 | C2 | semidirect |
| 4. #20292975 | C2 | semidirect |
| 5. #20292973 | C2 | semidirect |
| 6. #20292861 | C2 | semidirect |
| 7. C4×#13133803 | C2 | semidirect |
| 8. C2×C4×C107⋊C8 | C2 | semidirect |
| 9. #532×C107 | C2 | semidirect |
| 80. C2×C4×C107 | D8 | semidirect |
| 95. C107⋊C8 | #41 | semidirect |
| 121. C107 | #3169 | semidirect |
| 123. #532 | D107 | semidirect |
| 208. C2×C4 | #13133803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293177 | 2 |
| #20293030 | 2 |
| #20293003 | 2 |
| #20292975 | 2 |
| #20292973 | 2 |
| #20292861 | 2 |
| C4×#13133803 | 2 |
| C2×C4×C107⋊C8 | 2 |
| #532×C107 | 2 |
| #3169 | 107 |