Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
322 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20276934 | C2 | semidirect |
| 3. #20276929 | C2 | semidirect |
| 4. #20272702 | C2 | semidirect |
| 5. #20272699 | C2 | semidirect |
| 6. #20272653 | C2 | semidirect |
| 7. C53×#2098 | C2 | semidirect |
| 152. #2098 | D53 | semidirect |
| 180. C53 | #12303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285627 | 2 |
| #20276934 | 2 |
| #20276929 | 2 |
| #20272702 | 2 |
| #20272699 | 2 |
| #20272653 | 2 |
| C53×#2098 | 2 |
| #12303 | 53 |