Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 74 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. #20290207 | C2 | semidirect |
| 4. #20290024 | C2 | semidirect |
| 5. #20289579 | C2 | semidirect |
| 6. #20289571 | C2 | semidirect |
| 243. C53 | #9373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291606 | 2 |
| #20290235 | 2 |
| #20290207 | 2 |
| #20290024 | 2 |
| #20289579 | 2 |
| #20289571 | 2 |
| #20285727 | 2 |
| #9373 | 53 |