Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1078 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 2. C2×#16810992 | C2 | semidirect |
| 4. #20275867 | C2 | semidirect |
| 5. #20275684 | C2 | semidirect |
| 129. C22×C53 | #491 | semidirect |
| 174. C53 | #25912 | semidirect |
| 276. C22 | #16810992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133209 | 2 |
| C2×#16810992 | 2 |
| #20283067 | 2 |
| #20275867 | 2 |
| #20275684 | 2 |
| #20275020 | 2 |
| C53×#1749 | 2 |
| #25912 | 53 |