Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
376 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 5. #16810390 | C4 | semidirect |
| 7. C2×C4⋊C8×C53 | C4 | semidirect |
| 9. C2×C4×C8×C53 | C4 | semidirect |
| 116. C2×C4⋊C8 | Dic53 | semidirect |
| 119. C2×C4×C8 | Dic53 | semidirect |
| 122. C53 | #7237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274703 | 2 |
| C53×#1954 | 2 |
| #7237 | 53 |