Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. C2×#16810439 | C2 | semidirect |
| 5. #20272823 | C2 | semidirect |
| 6. #20272797 | C2 | semidirect |
| 7. C53×#1969 | C2 | semidirect |
| 11. #16811064 | C4 | semidirect |
| 176. #1969 | D53 | semidirect |
| 205. C53 | #13028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811064 | 2 |
| C2×#16810741 | 2 |
| C2×#16810439 | 2 |
| #20276425 | 2 |
| #20272823 | 2 |
| #20272797 | 2 |
| C53×#1969 | 2 |
| #13028 | 53 |