Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20273873 | C2 | semidirect |
| 4. #20273811 | C2 | semidirect |
| 5. #20273453 | C2 | semidirect |
| 6. #20273170 | C2 | semidirect |
| 7. C53×#3556 | C2 | semidirect |
| 152. #3556 | D53 | semidirect |
| 185. C53 | #18698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286098 | 2 |
| #20285040 | 2 |
| #20273873 | 2 |
| #20273811 | 2 |
| #20273453 | 2 |
| #20273170 | 2 |
| C53×#3556 | 2 |
| #18698 | 53 |