Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
130 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 41 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×#121 | C2 | semidirect |
| 2. C2×#90782 | C2 | semidirect |
| 3. #11745292 | C2 | semidirect |
| 4. C2×#90777 | C2 | semidirect |
| 5. #11745180 | C2 | semidirect |
| 6. #11745157 | C2 | semidirect |
| 7. #11745156 | C2 | semidirect |
| 37. #6597 | D4 | semidirect |
| 63. #121 | D29 | semidirect |
| 67. C29 | #469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#121 | 2 |
| C2×#90782 | 2 |
| #11745292 | 2 |
| C2×#90777 | 2 |
| #11745180 | 2 |
| #11745157 | 2 |
| #11745156 | 2 |
| #469 | 29 |