Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
698 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22×#13133158 | C2 | semidirect |
| 2. C2×#16811000 | C2 | semidirect |
| 3. C2×#16810423 | C2 | semidirect |
| 4. #20272793 | C2 | semidirect |
| 5. C53×#1970 | C2 | semidirect |
| 36. C2×#11719908 | D4 | semidirect |
| 41. C2×D8×C53 | D4 | semidirect |
| 109. C2×C4×C53 | D16 | semidirect |
| 149. #1970 | D53 | semidirect |
| 172. C53 | #13325 | semidirect |
| 188. C2×D8 | D212 | semidirect |
| 267. C2×C4 | #13133158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133158 | 2 |
| C2×#16811000 | 2 |
| C2×#16810423 | 2 |
| #20272793 | 2 |
| C53×#1970 | 2 |
| #13325 | 53 |