Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 366 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 |
|---|---|---|
| 11. #16811020 | C4 | semidirect |
| 33. #13133151 | Q8 | semidirect |
| 49. #108×C53 | Q8 | semidirect |
| 143. C53 | #13272 | semidirect |
| 162. #108 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811020 | 2 |
| C2×#16810443 | 2 |
| #20274597 | 2 |
| #20272822 | 2 |
| #20272821 | 2 |
| #20272815 | 2 |
| C53×#1383 | 2 |
| #13272 | 53 |