Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
540 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20283785 | C2 | semidirect |
| 3. #20273428 | C2 | semidirect |
| 4. #20273428 | C2 | semidirect |
| 5. #20273349 | C2 | semidirect |
| 6. #20272587 | C2 | semidirect |
| 7. C53×#1291 | C2 | semidirect |
| 164. #1291 | D53 | semidirect |
| 188. C53 | #9423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285167 | 2 |
| #20283785 | 2 |
| #20273428 | 2 |
| #20273349 | 2 |
| #20272587 | 2 |
| C53×#1291 | 2 |
| #9423 | 53 |