Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16810670 | C2 | semidirect |
| 3. #20276443 | C2 | semidirect |
| 4. C2×#16810404 | C2 | semidirect |
| 5. #20272830 | C2 | semidirect |
| 6. #20272829 | C2 | semidirect |
| 7. C53×#2143 | C2 | semidirect |
| 50. #13133153 | D4 | semidirect |
| 70. #108×C53 | D4 | semidirect |
| 182. #2143 | D53 | semidirect |
| 211. C53 | #12998 | semidirect |
| 251. #108 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284320 | 2 |
| C2×#16810670 | 2 |
| #20276443 | 2 |
| C2×#16810404 | 2 |
| #20272830 | 2 |
| #20272829 | 2 |
| C53×#2143 | 2 |
| #12998 | 53 |