Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 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 |
|---|---|---|
| 2. C4⋊C4×D29 | C2 | semidirect |
| 3. C29×#106 | C2 | semidirect |
| 4. #11745169 | C2 | semidirect |
| 5. #11745168 | C2 | semidirect |
| 6. #11745157 | C2 | semidirect |
| 7. #11745156 | C2 | semidirect |
| 56. #106 | D29 | semidirect |
| 60. C29 | #481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11745257 | 2 |
| C4⋊C4×D29 | 2 |
| C29×#106 | 2 |
| #11745169 | 2 |
| #11745168 | 2 |
| #11745157 | 2 |
| #11745156 | 2 |
| #481 | 29 |