Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×C42×C29 | C2 | semidirect |
| 3. #11745291 | C2 | semidirect |
| 4. C4×C22⋊D29 | C2 | semidirect |
| 5. #11745286 | C2 | semidirect |
| 6. #11745238 | C2 | semidirect |
| 7. #11745237 | C2 | semidirect |
| 8. C4×D116 | C2 | semidirect |
| 9. #11745234 | C2 | semidirect |
| 10. #11745232 | C2 | semidirect |
| 11. C4×Dic58 | C2 | semidirect |
| 85. C2×C42 | D29 | semidirect |
| 86. C29 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×C29 | 2 |
| #11745292 | 2 |
| #11745291 | 2 |
| C4×C22⋊D29 | 2 |
| #11745286 | 2 |
| #11745238 | 2 |
| #11745237 | 2 |
| C4×D116 | 2 |
| #11745234 | 2 |
| #11745232 | 2 |
| C4×Dic58 | 2 |
| #529 | 29 |