Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 103 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×#16811064 | C2 | semidirect |
| 2. C22×#13133160 | C2 | semidirect |
| 4. C2×#16810435 | C2 | semidirect |
| 5. C2×#16810429 | C2 | semidirect |
| 6. #20272804 | C2 | semidirect |
| 7. C53×#1979 | C2 | semidirect |
| 58. #13133157 | D4 | semidirect |
| 62. C2×#11719908 | D4 | semidirect |
| 69. C2×Q16×C53 | D4 | semidirect |
| 201. #1979 | D53 | semidirect |
| 232. C53 | #13338 | semidirect |
| 248. C2×Q16 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811064 | 2 |
| C22×#13133160 | 2 |
| #20285201 | 2 |
| C2×#16810435 | 2 |
| C2×#16810429 | 2 |
| #20272804 | 2 |
| C53×#1979 | 2 |
| #13338 | 53 |