Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
134 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 25 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 |
|---|---|---|
| 4. C53⋊#564 | C4 | semidirect |
| 7. #16810365 | C4 | semidirect |
| 75. C53 | #7524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274016 | 2 |
| #20272886 | 2 |
| C53×#1355 | 2 |
| #7524 | 53 |