Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 118 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. #20289682 | C2 | semidirect |
| 51. C2×Dic106 | C16 | semidirect |
| 135. C53 | #11637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291072 | 2 |
| #20289682 | 2 |
| C2×#16810747 | 2 |
| #11637 | 53 |