Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
310 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 155 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. C29×#117 | C2 | semidirect |
| 3. C2×C4×Dic29 | C2 | semidirect |
| 4. #11745255 | C2 | semidirect |
| 5. #11745249 | C2 | semidirect |
| 6. #11745243 | C2 | semidirect |
| 7. #11745234 | C2 | semidirect |
| 8. C42×D29 | C2 | semidirect |
| 12. #90805 | C4 | semidirect |
| 28. C2×C4×C29 | C2×C4 | semidirect |
| 32. C22⋊D29 | C2×C4 | semidirect |
| 37. D116 | C2×C4 | semidirect |
| 39. C4×D29 | C2×C4 | semidirect |
| 40. Dic58 | C2×C4 | semidirect |
| 51. Dic29 | #41 | semidirect |
| 62. #117 | D29 | semidirect |
| 65. C29 | C4×#41 | semidirect |
| 94. C2×C4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90805 | 2 |
| C29×#117 | 2 |
| C2×C4×Dic29 | 2 |
| #11745255 | 2 |
| #11745249 | 2 |
| #11745243 | 2 |
| #11745234 | 2 |
| C42×D29 | 2 |
| C4×#41 | 29 |