Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 71 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×#16810418 | C2 | semidirect |
| 3. #20272876 | C2 | semidirect |
| 4. #20272873 | C2 | semidirect |
| 5. C2×C53×#355 | C2 | semidirect |
| 8. #16811173 | C4 | semidirect |
| 9. #16811018 | C4 | semidirect |
| 11. #16811013 | C4 | semidirect |
| 16. C4×#11719917 | C4 | semidirect |
| 37. #13133217 | C2×C4 | semidirect |
| 38. #13133214 | C2×C4 | semidirect |
| 45. #13133128 | C2×C4 | semidirect |
| 46. #13133128 | C2×C4 | semidirect |
| 171. C2×#355 | D53 | semidirect |
| 199. C53 | #13578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285179 | 2 |
| C2×#16810418 | 2 |
| #20272876 | 2 |
| #20272873 | 2 |
| C2×C53×#355 | 2 |
| #13578 | 53 |