Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20293394 | C2 | semidirect |
| 2. #20292644 | C2 | semidirect |
| 3. #20292623 | C2 | semidirect |
| 4. #20292594 | C2 | semidirect |
| 5. #20292399 | C2 | semidirect |
| 6. #20292391 | C2 | semidirect |
| 22. #137×C107 | C4 | semidirect |
| 24. AGL(1,ℤ/8)×C107 | C4 | semidirect |
| 119. C107 | #1881 | semidirect |
| 130. #137 | Dic107 | semidirect |
| 132. AGL(1,ℤ/8) | Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293394 | 2 |
| #20292644 | 2 |
| #20292623 | 2 |
| #20292594 | 2 |
| #20292399 | 2 |
| #20292391 | 2 |
| #575×C107 | 2 |
| #1881 | 107 |