Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20293029 | C2 | semidirect |
| 3. #20292969 | C2 | semidirect |
| 4. #20292963 | C2 | semidirect |
| 5. #20292935 | C2 | semidirect |
| 6. #20292885 | C2 | semidirect |
| 7. C4×Dic428 | C2 | semidirect |
| 8. #20292669 | C2 | semidirect |
| 97. C107 | #3352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293317 | 2 |
| #20293029 | 2 |
| #20292969 | 2 |
| #20292963 | 2 |
| #20292935 | 2 |
| #20292885 | 2 |
| C4×Dic428 | 2 |
| #20292669 | 2 |
| #436×C107 | 2 |
| #3352 | 107 |