Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
650 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 650 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×#16811058 | C2 | semidirect |
| 2. C2×#16811000 | C2 | semidirect |
| 3. C2×#16810435 | C2 | semidirect |
| 4. #20272797 | C2 | semidirect |
| 5. C53×#1974 | C2 | semidirect |
| 37. #13133157 | D4 | semidirect |
| 42. C2×Q16×C53 | D4 | semidirect |
| 44. C2×D8×C53 | D4 | semidirect |
| 145. #1974 | D53 | semidirect |
| 168. C53 | #13331 | semidirect |
| 174. C2×Q16 | D212 | semidirect |
| 185. C2×D8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811058 | 2 |
| C2×#16811000 | 2 |
| C2×#16810435 | 2 |
| #20272797 | 2 |
| C53×#1974 | 2 |
| #13331 | 53 |