Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1446 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1446 conjugacy classes of subgroups — too many to draw. Only its 280 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. #20290609 | C2 | semidirect |
| 3. #20290378 | C2 | semidirect |
| 8. #16811489 | C22 | semidirect |
| 144. C53 | #20683 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811595 | 2 |
| #20290609 | 2 |
| #20290378 | 2 |
| C22×#13133175 | 2 |
| #20683 | 53 |