Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 64 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. #20289855 | C2 | direct (N × H) |
| 9. #16810989 | C4 | semidirect |
| 12. C2×#13133128 | C4 | semidirect |
| 13. C2×#125×C53 | C4 | semidirect |
| 27. #13133128 | C2×C4 | semidirect |
| 30. #125×C53 | C2×C4 | semidirect |
| 106. C2×C53 | #1412 | semidirect |
| 111. C2×#125 | #6157 | semidirect |
| 120. C53 | C2×#1412 | semidirect |
| 130. #125 | C2×#6157 | semidirect |
| 211. C2 | #20289855 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811528 | 2 |
| #20289855 | 2 |
| C2×#16810989 | 2 |
| C2×#1412 | 53 |