Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #20292637 | C2 | semidirect |
| 5. C2×#16812027 | C2 | semidirect |
| 6. #20292398 | C2 | semidirect |
| 7. #338×C107 | C2 | semidirect |
| 12. C2×Dic428 | C4 | semidirect |
| 13. C2×#13133807 | C4 | semidirect |
| 108. C107 | #1902 | semidirect |
| 115. #338 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812142 | 2 |
| #20293393 | 2 |
| #20292643 | 2 |
| #20292637 | 2 |
| C2×#16812027 | 2 |
| #20292398 | 2 |
| #338×C107 | 2 |
| #1902 | 107 |