Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
774 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 167 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. #20273405 | C2 | semidirect |
| 4. #20273170 | C2 | semidirect |
| 187. C53 | #8355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275510 | 2 |
| #20274707 | 2 |
| #20273405 | 2 |
| #20273170 | 2 |
| C53×#3501 | 2 |
| #8355 | 53 |