Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16810435 | C2 | semidirect |
| 3. #20276443 | C2 | semidirect |
| 4. #20275625 | C2 | semidirect |
| 5. #20272818 | C2 | semidirect |
| 6. #20272801 | C2 | semidirect |
| 7. C53×#2957 | C2 | semidirect |
| 11. C2×#13133160 | C4 | semidirect |
| 12. C2×#13133158 | C4 | semidirect |
| 166. #2957 | D53 | semidirect |
| 197. C53 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811058 | 2 |
| C2×#16810435 | 2 |
| #20276443 | 2 |
| #20275625 | 2 |
| #20272818 | 2 |
| #20272801 | 2 |
| C53×#2957 | 2 |
| #13036 | 53 |