Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20275184 | C2 | semidirect |
| 3. #20274897 | C2 | semidirect |
| 4. #20273235 | C2 | semidirect |
| 6. #20272592 | C2 | semidirect |
| 252. C53 | #10558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275184 | 2 |
| #20275179 | 2 |
| #20274897 | 2 |
| #20273235 | 2 |
| #20273231 | 2 |
| #20272592 | 2 |
| C53×#3187 | 2 |
| #10558 | 53 |