Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 1. #20291682 | C2 | semidirect |
| 2. #20290959 | C2 | semidirect |
| 3. #20290957 | C2 | semidirect |
| 4. #20290953 | C2 | semidirect |
| 5. #20289762 | C2 | semidirect |
| 6. #20289756 | C2 | semidirect |
| 208. C53 | #12986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291682 | 2 |
| #20290959 | 2 |
| #20290957 | 2 |
| #20290953 | 2 |
| #20289762 | 2 |
| #20289756 | 2 |
| C2×#16810742 | 2 |
| #12986 | 53 |