Finite Group DatabasebetaFinite Group DatabasebetaOrder 704.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. C2×C11×M16 | C2 | semidirect |
| 3. C2×C4×Dic11 | C2 | semidirect |
| 4. #66889 | C2 | direct (N × H) |
| 10. #4339 | C4 | semidirect |
| 12. C2×D44 | C4 | semidirect |
| 14. C2×Dic22 | C4 | semidirect |
| 16. C11×M16 | C22 | semidirect |
| 19. C4×Dic11 | C22 | semidirect |
| 34. D44 | C2×C4 | semidirect |
| 38. Dic22 | C2×C4 | semidirect |
| 54. C2×M16 | D11 | semidirect |
| 59. C2×C11 | #104 | semidirect |
| 73. M16 | C2×D11 | semidirect |
| 77. C11 | C2×#104 | semidirect |
| 113. C2 | #66889 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4339 | 2 |
| C2×C11×M16 | 2 |
| C2×C4×Dic11 | 2 |
| #66889 | 2 |
| C2×#104 | 11 |