Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #20283326 | C2 | semidirect |
| 3. #20276930 | C2 | semidirect |
| 4. #20276488 | C2 | semidirect |
| 5. C2×#16810437 | C2 | semidirect |
| 6. C53×#2115 | C2 | semidirect |
| 13. #16810672 | C22 | semidirect |
| 18. #16810446 | C22 | semidirect |
| 22. C53×#349 | C22 | semidirect |
| 131. #2115 | D53 | semidirect |
| 152. #349 | C2×D53 | semidirect |
| 153. C53 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284363 | 2 |
| #20283326 | 2 |
| #20276930 | 2 |
| #20276488 | 2 |
| C2×#16810437 | 2 |
| C53×#2115 | 2 |
| #33657 | 53 |