Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16810427 | C2 | semidirect |
| 5. #20272824 | C2 | semidirect |
| 6. #20272808 | C2 | semidirect |
| 7. C2×C53×#362 | C2 | semidirect |
| 16. #16810895 | C4 | semidirect |
| 167. C2×#362 | D53 | semidirect |
| 198. C53 | #13072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811041 | 2 |
| C2×#16810895 | 2 |
| C2×#16810427 | 2 |
| #20274776 | 2 |
| #20272824 | 2 |
| #20272808 | 2 |
| C2×C53×#362 | 2 |
| #13072 | 53 |