Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20274759 | C2 | semidirect |
| 4. #20272836 | C2 | semidirect |
| 5. C53×#1391 | C2 | semidirect |
| 6. C2×#13133225 | C4 | semidirect |
| 12. #16810646 | C4 | semidirect |
| 14. #16810589 | C4 | semidirect |
| 15. C2×C8×Dic53 | C4 | semidirect |
| 150. #1391 | D53 | semidirect |
| 171. C53 | #12807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283423 | 2 |
| #20276378 | 2 |
| #20274759 | 2 |
| #20272836 | 2 |
| C53×#1391 | 2 |
| #12807 | 53 |