Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 108 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. C2×#16811550 | C2 | semidirect |
| 2. C2×#16811549 | C2 | semidirect |
| 4. #20289773 | C2 | semidirect |
| 13. C2×#13133157 | C4 | semidirect |
| 14. C2×#13133156 | C4 | semidirect |
| 15. C2×#13133156 | C4 | semidirect |
| 20. C2×M32×C53 | C4 | semidirect |
| 89. C16×C53 | C22⋊C4 | semidirect |
| 91. #11719908 | C22⋊C4 | semidirect |
| 168. C2×M32 | #6157 | semidirect |
| 177. C53 | #12836 | semidirect |
| 248. C16 | C22⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811550 | 2 |
| C2×#16811549 | 2 |
| #20290592 | 2 |
| #20289773 | 2 |
| C2×M32×D53 | 2 |
| #12836 | 53 |