Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
388 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20275466 | C2 | semidirect |
| 5. #20272829 | C2 | semidirect |
| 6. #20272798 | C2 | semidirect |
| 7. C53×#2161 | C2 | semidirect |
| 17. #16810434 | C4 | semidirect |
| 140. #2161 | D53 | semidirect |
| 167. C53 | #12944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810744 | 2 |
| #20276452 | 2 |
| #20276442 | 2 |
| #20275466 | 2 |
| #20272829 | 2 |
| #20272798 | 2 |
| C53×#2161 | 2 |
| #12944 | 53 |