Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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. C22×Dic58 | C2 | semidirect |
| 3. C2×M16×C29 | C2 | semidirect |
| 4. #11745271 | C2 | direct (N × H) |
| 5. C2×Dic116 | C2 | semidirect |
| 6. C2×#90773 | C2 | semidirect |
| 18. C2×Dic58 | C22 | semidirect |
| 19. M16×C29 | C22 | semidirect |
| 21. Dic116 | C22 | semidirect |
| 22. #90773 | C22 | semidirect |
| 54. C2×C29 | #137 | semidirect |
| 62. C2×M16 | D29 | semidirect |
| 63. C29 | C2×#137 | semidirect |
| 78. M16 | C2×D29 | semidirect |
| 111. C2 | #11745271 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90805 | 2 |
| C22×Dic58 | 2 |
| C2×M16×C29 | 2 |
| #11745271 | 2 |
| C2×Dic116 | 2 |
| C2×#90773 | 2 |
| C2×#137 | 29 |