Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20292665 | C2 | semidirect |
| 3. #20292643 | C2 | semidirect |
| 4. #20292600 | C2 | semidirect |
| 5. #405×C107 | C2 | semidirect |
| 11. C2×Dic428 | C4 | semidirect |
| 12. C2×#13133807 | C4 | semidirect |
| 13. C2×D856 | C4 | semidirect |
| 97. C107 | #1976 | semidirect |
| 102. #405 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| #20292665 | 2 |
| #20292643 | 2 |
| #20292600 | 2 |
| #405×C107 | 2 |
| #1976 | 107 |