Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
610 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 610 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. #20280504 | C2 | semidirect |
| 3. #20275552 | C2 | semidirect |
| 4. #20274814 | C2 | semidirect |
| 5. #20273232 | C2 | semidirect |
| 6. #20272622 | C2 | semidirect |
| 7. C53×#3094 | C2 | semidirect |
| 228. #3094 | D53 | semidirect |
| 268. C53 | #9932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285512 | 2 |
| #20280504 | 2 |
| #20275552 | 2 |
| #20274814 | 2 |
| #20273232 | 2 |
| #20272622 | 2 |
| C53×#3094 | 2 |
| #9932 | 53 |