Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. C22×#13133157 | C2 | semidirect |
| 3. C2×#16810423 | C2 | semidirect |
| 4. #20272806 | C2 | semidirect |
| 5. C53×#1808 | C2 | semidirect |
| 12. #16810859 | C4 | semidirect |
| 33. C2×#11719908 | D4 | semidirect |
| 142. #1808 | D53 | semidirect |
| 165. C53 | #13061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133157 | 2 |
| C2×#16810859 | 2 |
| C2×#16810423 | 2 |
| #20272806 | 2 |
| C53×#1808 | 2 |
| #13061 | 53 |