Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1854 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1854 conjugacy classes of subgroups — too many to draw. Only its 331 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×#16810487 | C2 | semidirect |
| 3. #20272986 | C2 | semidirect |
| 4. #20272959 | C2 | semidirect |
| 6. C53×#1446 | C2 | semidirect |
| 9. C2×#13133206 | C4 | semidirect |
| 86. C4×Dic53 | C22⋊C4 | semidirect |
| 150. #1446 | D53 | semidirect |
| 173. C53 | #14662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133206 | 2 |
| C2×#16810487 | 2 |
| #20272986 | 2 |
| #20272959 | 2 |
| #20272955 | 2 |
| C53×#1446 | 2 |
| #14662 | 53 |