Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
426 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 70 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. #20290687 | C2 | semidirect |
| 4. #20290672 | C2 | semidirect |
| 5. #20289814 | C2 | semidirect |
| 6. #20289805 | C2 | semidirect |
| 237. C53 | #12962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291589 | 2 |
| #20290727 | 2 |
| #20290687 | 2 |
| #20290672 | 2 |
| #20289814 | 2 |
| #20289805 | 2 |
| #20276355 | 2 |
| #12962 | 53 |