Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
588 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 122 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×#16811483 | C2 | semidirect |
| 4. #20289593 | C2 | semidirect |
| 222. C53 | #9128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811640 | 2 |
| #20290571 | 2 |
| C2×#16811483 | 2 |
| #20289593 | 2 |
| #20283063 | 2 |
| #9128 | 53 |