Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 80 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. #20290598 | C2 | semidirect |
| 3. #20289804 | C2 | semidirect |
| 10. C2×#13133225 | C4 | semidirect |
| 15. #16810591 | C4 | semidirect |
| 17. C2×C4×#88322 | C4 | semidirect |
| 18. C53×#423 | C4 | semidirect |
| 151. #423 | #6157 | semidirect |
| 159. C53 | #12807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290988 | 2 |
| #20290598 | 2 |
| #20289804 | 2 |
| #20283426 | 2 |
| #12807 | 53 |