Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
286 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20292669 | C2 | semidirect |
| 4. #20292493 | C2 | semidirect |
| 5. #20292395 | C2 | semidirect |
| 6. #20292387 | C2 | semidirect |
| 25. #104×C107 | C4 | semidirect |
| 54. M16×C107 | C2×C4 | semidirect |
| 57. C42×C107 | C2×C4 | semidirect |
| 112. C107 | #1860 | semidirect |
| 134. #104 | Dic107 | semidirect |
| 154. M16 | C2×Dic107 | semidirect |
| 169. C42 | C2×Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293110 | 2 |
| #20292669 | 2 |
| #20292628 | 2 |
| #20292493 | 2 |
| #20292395 | 2 |
| #20292387 | 2 |
| C2×#104×C107 | 2 |
| #1860 | 107 |