Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20293000 | C2 | semidirect |
| 2. #20292908 | C2 | semidirect |
| 4. C8×D428 | C2 | semidirect |
| 5. #20292372 | C2 | semidirect |
| 6. #20292370 | C2 | semidirect |
| 7. #334×C107 | C2 | semidirect |
| 56. D428 | SD16 | semidirect |
| 64. C8×C107 | D8 | semidirect |
| 86. C107 | #1665 | semidirect |
| 91. #334 | D107 | semidirect |
| 151. C8 | D856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293000 | 2 |
| #20292908 | 2 |
| #20292823 | 2 |
| C8×D428 | 2 |
| #20292372 | 2 |
| #20292370 | 2 |
| #334×C107 | 2 |
| #1665 | 107 |