Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
712 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 712 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 |
|---|---|---|
| 1. C2×#16810910 | C2 | semidirect |
| 3. C2×#16810352 | C2 | semidirect |
| 4. #20272598 | C2 | semidirect |
| 5. C53×#1956 | C2 | semidirect |
| 35. C4⋊#88322 | D4 | semidirect |
| 42. C4⋊Q8×C53 | D4 | semidirect |
| 155. #1956 | D53 | semidirect |
| 178. C53 | #10235 | semidirect |
| 187. C4⋊Q8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810910 | 2 |
| #20279631 | 2 |
| C2×#16810352 | 2 |
| #20272598 | 2 |
| C53×#1956 | 2 |
| #10235 | 53 |