Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16810447 | C2 | semidirect |
| 4. #20275466 | C2 | semidirect |
| 5. #20272821 | C2 | semidirect |
| 6. #20272794 | C2 | semidirect |
| 18. #16810424 | C4 | semidirect |
| 34. C2×#11719908 | C2×C4 | semidirect |
| 35. #13133151 | C2×C4 | semidirect |
| 168. C53 | #12956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810735 | 2 |
| C2×#16810447 | 2 |
| #20276431 | 2 |
| #20275466 | 2 |
| #20272821 | 2 |
| #20272794 | 2 |
| C2×C53×#361 | 2 |
| #12956 | 53 |