Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
270 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #16811390 | C4 | semidirect |
| 7. #16810597 | C4 | semidirect |
| 10. #16810363 | C4 | semidirect |
| 14. C53×#353 | C4 | semidirect |
| 128. #353 | Dic53 | semidirect |
| 132. C53 | #7494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275099 | 2 |
| #20273350 | 2 |
| C53×#2126 | 2 |
| #7494 | 53 |