Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
622 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 16. #16810380 | C4 | semidirect |
| 17. #16810379 | C4 | semidirect |
| 18. C53×H(3,ℤ/4) | C4 | semidirect |
| 176. H(3,ℤ/4) | #6157 | semidirect |
| 178. C53 | #11286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#430 | 2 |
| #20290423 | 2 |
| #20290391 | 2 |
| #20290377 | 2 |
| H(3,ℤ/4)×D53 | 2 |
| #11286 | 53 |