Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
546 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. C2×#16810439 | C2 | semidirect |
| 4. #20272797 | C2 | semidirect |
| 5. C2×C53×#494 | C2 | semidirect |
| 137. C2×#494 | D53 | semidirect |
| 161. C53 | #13333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811064 | 2 |
| C2×#16810439 | 2 |
| #20275603 | 2 |
| #20272797 | 2 |
| C2×C53×#494 | 2 |
| #13333 | 53 |