Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
104 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 39 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. C29×#131 | C2 | semidirect |
| 2. #11745313 | C2 | semidirect |
| 4. C2×#90773 | C2 | semidirect |
| 5. #11745172 | C2 | semidirect |
| 6. #11745171 | C2 | semidirect |
| 7. #11745167 | C2 | semidirect |
| 55. #131 | D29 | semidirect |
| 59. C29 | #471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#131 | 2 |
| #11745313 | 2 |
| #11745311 | 2 |
| C2×#90773 | 2 |
| #11745172 | 2 |
| #11745171 | 2 |
| #11745167 | 2 |
| #471 | 29 |