Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #20273498 | C2 | semidirect |
| 5. #20272615 | C2 | semidirect |
| 6. #20272613 | C2 | semidirect |
| 7. C53×#1573 | C2 | semidirect |
| 185. #1573 | D53 | semidirect |
| 217. C53 | #8864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283743 | 2 |
| #20275512 | 2 |
| #20273498 | 2 |
| #20273035 | 2 |
| #20272615 | 2 |
| #20272613 | 2 |
| C53×#1573 | 2 |
| #8864 | 53 |