Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20273420 | C2 | semidirect |
| 3. #20273338 | C2 | semidirect |
| 4. #20273068 | C2 | semidirect |
| 5. #20272627 | C2 | semidirect |
| 6. #20272576 | C2 | semidirect |
| 7. C53×#2980 | C2 | semidirect |
| 161. #2980 | D53 | semidirect |
| 192. C53 | #9333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285698 | 2 |
| #20273420 | 2 |
| #20273338 | 2 |
| #20273068 | 2 |
| #20272627 | 2 |
| #20272576 | 2 |
| C53×#2980 | 2 |
| #9333 | 53 |