Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 3. C4×Dic58 | C2 | semidirect |
| 4. C29×#97 | C2 | semidirect |
| 6. #11745166 | C2 | semidirect |
| 7. #11745164 | C2 | semidirect |
| 19. #90773 | C4 | semidirect |
| 31. Dic58 | C2×C4 | semidirect |
| 33. C8×C29 | C2×C4 | semidirect |
| 56. #97 | D29 | semidirect |
| 57. C29 | #440 | semidirect |
| 83. C8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90773 | 2 |
| C4×D116 | 2 |
| C4×Dic58 | 2 |
| C29×#97 | 2 |
| #11745169 | 2 |
| #11745166 | 2 |
| #11745164 | 2 |
| #440 | 29 |