Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
440 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20273486 | C2 | semidirect |
| 4. #20273387 | C2 | semidirect |
| 6. #20272610 | C2 | semidirect |
| 7. C53×#1546 | C2 | semidirect |
| 169. #1546 | D53 | semidirect |
| 195. C53 | #10445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810825 | 2 |
| #20274704 | 2 |
| #20273486 | 2 |
| #20273387 | 2 |
| #20273105 | 2 |
| #20272610 | 2 |
| C53×#1546 | 2 |
| #10445 | 53 |