Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
726 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 293 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×#16812116 | C2 | semidirect |
| 2. #20293110 | C2 | semidirect |
| 3. #20292636 | C2 | semidirect |
| 4. #20292628 | C2 | semidirect |
| 5. #20292623 | C2 | semidirect |
| 6. C2×#16812033 | C2 | semidirect |
| 21. 2−1+4×C107 | C4 | semidirect |
| 40. #41×C107 | C2×C4 | semidirect |
| 45. C2×Q8×C107 | C2×C4 | semidirect |
| 95. C107 | #2898 | semidirect |
| 104. 2−1+4 | Dic107 | semidirect |
| 125. #41 | C2×Dic107 | semidirect |
| 130. C2×Q8 | C2×Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812116 | 2 |
| #20293110 | 2 |
| #20292636 | 2 |
| #20292628 | 2 |
| #20292623 | 2 |
| C2×#16812033 | 2 |
| C2×2−1+4×C107 | 2 |
| #2898 | 107 |