Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
786 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 3. #20274042 | C2 | semidirect |
| 161. C53 | #19008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C53⋊#564 | 2 |
| #20285917 | 2 |
| #20274042 | 2 |
| #20273342 | 2 |
| #20273316 | 2 |
| C53×#3166 | 2 |
| #19008 | 53 |