Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20293352 | C2 | semidirect |
| 3. #20292980 | C2 | semidirect |
| 4. #20292925 | C2 | semidirect |
| 5. #20292909 | C2 | semidirect |
| 6. #20292848 | C2 | semidirect |
| 8. C8×Dic214 | C2 | semidirect |
| 9. C4×Dic428 | C2 | semidirect |
| 10. #20292718 | C2 | semidirect |
| 118. C107 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293363 | 2 |
| #20293352 | 2 |
| #20292980 | 2 |
| #20292925 | 2 |
| #20292909 | 2 |
| #20292848 | 2 |
| #20292824 | 2 |
| C8×Dic214 | 2 |
| C4×Dic428 | 2 |
| #20292718 | 2 |
| #486×C107 | 2 |
| #3365 | 107 |