Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
960 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 147 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. #20275532 | C2 | semidirect |
| 2. C2×#16810363 | C2 | semidirect |
| 6. C2×#13133128 | C22 | semidirect |
| 7. #16810493 | C22 | semidirect |
| 10. C53×H(3,𝔽4) | C4 | semidirect |
| 108. H(3,𝔽4) | Dic53 | semidirect |
| 117. C53 | #8506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275532 | 2 |
| C2×#16810363 | 2 |
| C2×C53×H(3,𝔽4) | 2 |
| #8506 | 53 |