Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
386 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 3. #20289672 | C2 | semidirect |
| 28. C2×Dic212 | C8 | semidirect |
| 140. C53 | #11594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290921 | 2 |
| #20290262 | 2 |
| #20289672 | 2 |
| C2×#16810717 | 2 |
| #11594 | 53 |