Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20275687 | C2 | semidirect |
| 4. #20273401 | C2 | semidirect |
| 6. #20272545 | C2 | semidirect |
| 7. C53×#1286 | C2 | semidirect |
| 11. #16810996 | C4 | semidirect |
| 12. #16810974 | C4 | semidirect |
| 108. C2×#88322 | SD16 | semidirect |
| 174. #1286 | D53 | semidirect |
| 201. C53 | #9289 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285642 | 2 |
| #20283432 | 2 |
| #20275687 | 2 |
| #20273401 | 2 |
| #20273274 | 2 |
| #20272545 | 2 |
| C53×#1286 | 2 |
| #9289 | 53 |