Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
648 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20273292 | C2 | semidirect |
| 2. #20273123 | C2 | semidirect |
| 4. #16810676 | C22 | semidirect |
| 5. #16810491 | C22 | semidirect |
| 10. C53×#563 | C4 | semidirect |
| 11. C53×H(3,𝔽4) | C4 | semidirect |
| 122. #563 | Dic53 | semidirect |
| 123. H(3,𝔽4) | Dic53 | semidirect |
| 135. C53 | #8514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20273292 | 2 |
| #20273123 | 2 |
| C53×#3568 | 2 |
| #8514 | 53 |