Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
544 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20284655 | C2 | semidirect |
| 3. #20274786 | C2 | semidirect |
| 4. #20273076 | C2 | semidirect |
| 5. #20273075 | C2 | semidirect |
| 6. #20272591 | C2 | semidirect |
| 7. C53×#3094 | C2 | semidirect |
| 207. #3094 | D53 | semidirect |
| 245. C53 | #9977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285463 | 2 |
| #20284655 | 2 |
| #20274786 | 2 |
| #20273076 | 2 |
| #20273075 | 2 |
| #20272591 | 2 |
| C53×#3094 | 2 |
| #9977 | 53 |