Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20276944 | C2 | semidirect |
| 4. #20272763 | C2 | semidirect |
| 5. Q8⋊#11719908 | C2 | semidirect |
| 7. C53×#1674 | C2 | semidirect |
| 126. #1674 | D53 | semidirect |
| 151. C53 | #12383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287704 | 2 |
| #20276944 | 2 |
| #20276849 | 2 |
| #20272763 | 2 |
| Q8⋊#11719908 | 2 |
| #20272675 | 2 |
| C53×#1674 | 2 |
| #12383 | 53 |