Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
814 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. C2×#16810365 | C2 | semidirect |
| 4. C2×#16810364 | C2 | semidirect |
| 5. C2×C53×#330 | C2 | semidirect |
| 158. C2×#330 | D53 | semidirect |
| 182. C53 | #8338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811179 | 2 |
| #20274478 | 2 |
| C2×#16810365 | 2 |
| C2×#16810364 | 2 |
| C2×C53×#330 | 2 |
| #8338 | 53 |