Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
784 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20274042 | C2 | semidirect |
| 163. C53 | #19067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289210 | 2 |
| #20285925 | 2 |
| #20274042 | 2 |
| #20273353 | 2 |
| #20273329 | 2 |
| C53×#3162 | 2 |
| #19067 | 53 |