Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
458 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 8. #16810993 | C4 | semidirect |
| 138. C53 | #9004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810993 | 2 |
| #20275687 | 2 |
| C2×#16810365 | 2 |
| #20272596 | 2 |
| C53×#2382 | 2 |
| #9004 | 53 |