Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20272885 | C2 | direct (N × H) |
| 5. C2×#13133209 | C4 | semidirect |
| 8. #16810987 | C4 | semidirect |
| 13. C2×#13133128 | C4 | semidirect |
| 23. #13133209 | C2×C4 | semidirect |
| 34. #13133128 | C2×C4 | semidirect |
| 152. C2×C53 | #1412 | semidirect |
| 169. C53 | C2×#1412 | semidirect |
| 297. C2 | #20272885 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810987 | 2 |
| C2×#16810416 | 2 |
| #20272885 | 2 |
| C2×C53×#353 | 2 |
| C2×#1412 | 53 |