Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20276380 | C2 | semidirect |
| 2. #20272880 | C2 | semidirect |
| 3. #20272878 | C2 | semidirect |
| 9. C53×#532 | C4 | semidirect |
| 12. C53×#494 | C4 | semidirect |
| 14. C53×#492 | C4 | semidirect |
| 16. C2×C4×C8×C53 | C4 | semidirect |
| 130. #532 | Dic53 | semidirect |
| 133. #494 | Dic53 | semidirect |
| 135. #492 | Dic53 | semidirect |
| 138. C2×C4×C8 | Dic53 | semidirect |
| 141. C53 | #13583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276380 | 2 |
| #20272880 | 2 |
| #20272878 | 2 |
| C53×#3147 | 2 |
| #13583 | 53 |