Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
932 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#16810420 | C2 | semidirect |
| 2. #20275119 | C2 | semidirect |
| 4. #16811101 | C22 | semidirect |
| 6. C2×#13133136 | C22 | semidirect |
| 10. C53×H(3,𝔽4) | C4 | semidirect |
| 110. H(3,𝔽4) | Dic53 | semidirect |
| 119. C53 | #12774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810420 | 2 |
| #20275119 | 2 |
| C2×C53×H(3,𝔽4) | 2 |
| #12774 | 53 |