Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1012 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 1012 conjugacy classes of subgroups — too many to draw. Only its 208 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. #20291566 | C2 | semidirect |
| 2. #20289991 | C2 | semidirect |
| 3. #20289980 | C2 | semidirect |
| 4. #20289975 | C2 | semidirect |
| 5. #20289968 | C2 | semidirect |
| 214. C53 | #17408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291566 | 2 |
| #20289991 | 2 |
| #20289980 | 2 |
| #20289975 | 2 |
| #20289968 | 2 |
| C2×#16811227 | 2 |
| #17408 | 53 |