Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
204 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. C2×#16810462 | C2 | semidirect |
| 2. #20276806 | C2 | semidirect |
| 4. #20272917 | C2 | semidirect |
| 5. #20272897 | C2 | semidirect |
| 6. #20272894 | C2 | semidirect |
| 7. C22×C32×C53 | C2 | semidirect |
| 39. C32×C53 | D4 | semidirect |
| 80. C22×C53 | SD64 | semidirect |
| 92. C22×C32 | D53 | semidirect |
| 116. C53 | #13696 | semidirect |
| 135. C32 | C22⋊D53 | semidirect |
| 178. C22 | #16810462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810462 | 2 |
| #20276806 | 2 |
| #20276801 | 2 |
| #20272917 | 2 |
| #20272897 | 2 |
| #20272894 | 2 |
| C22×C32×C53 | 2 |
| #13696 | 53 |