Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
888 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20275544 | C2 | semidirect |
| 2. #20273450 | C2 | semidirect |
| 4. #16810647 | C22 | semidirect |
| 6. C42×Dic53 | C22 | semidirect |
| 9. C53×H(3,𝔽4) | C4 | semidirect |
| 90. H(3,𝔽4) | Dic53 | semidirect |
| 100. C53 | #8530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275544 | 2 |
| #20273450 | 2 |
| C53×#3549 | 2 |
| #8530 | 53 |