Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
176 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 51 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. #20292974 | C2 | semidirect |
| 2. #20292833 | C2 | semidirect |
| 4. #20292706 | C2 | semidirect |
| 5. #20292374 | C2 | semidirect |
| 6. #20292370 | C2 | semidirect |
| 7. #334×C107 | C2 | semidirect |
| 85. C107 | #1701 | semidirect |
| 90. #334 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292974 | 2 |
| #20292833 | 2 |
| #20292823 | 2 |
| #20292706 | 2 |
| #20292374 | 2 |
| #20292370 | 2 |
| #334×C107 | 2 |
| #1701 | 107 |