Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#16810731 | C2 | semidirect |
| 3. C2×#16810440 | C2 | semidirect |
| 6. #20272814 | C2 | semidirect |
| 7. C53×#1375 | C2 | semidirect |
| 13. C2×Dic424 | C4 | semidirect |
| 14. C2×#13133162 | C4 | semidirect |
| 171. #1375 | D53 | semidirect |
| 196. C53 | #13038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811066 | 2 |
| C2×#16810731 | 2 |
| C2×#16810440 | 2 |
| C2×#16810434 | 2 |
| #20275608 | 2 |
| #20272814 | 2 |
| C53×#1375 | 2 |
| #13038 | 53 |