Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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. C22×#6597 | C2 | semidirect |
| 5. #11745180 | C2 | semidirect |
| 6. #11745157 | C2 | semidirect |
| 7. #11745155 | C2 | semidirect |
| 37. #6597 | D4 | semidirect |
| 43. C22×C29 | D8 | semidirect |
| 63. #121 | D29 | semidirect |
| 67. C29 | #466 | semidirect |
| 106. C22 | #90782 | 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 |
| C22×#6597 | 2 |
| #11745180 | 2 |
| #11745157 | 2 |
| #11745155 | 2 |
| #466 | 29 |