Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
448 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 5. C2×#13133217 | C4 | semidirect |
| 9. #16810543 | C4 | semidirect |
| 12. #16810489 | C4 | semidirect |
| 171. C53 | #11717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280536 | 2 |
| #20274448 | 2 |
| #20272737 | 2 |
| C53×#1458 | 2 |
| #11717 | 53 |