Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
188 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 47 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. C29×C22⋊Q8 | C2 | semidirect |
| 3. C2×#90784 | C2 | semidirect |
| 4. C22⋊#6597 | C2 | semidirect |
| 5. #11745157 | C2 | semidirect |
| 7. C2×Q8×C29 | C22 | semidirect |
| 13. C4⋊C4×C29 | C22 | semidirect |
| 16. C2×#6597 | C22 | semidirect |
| 34. C22×C29 | SD16 | semidirect |
| 52. C22⋊Q8 | D29 | semidirect |
| 55. C29 | #450 | semidirect |
| 57. C2×Q8 | C2×D29 | semidirect |
| 65. C4⋊C4 | C2×D29 | semidirect |
| 88. C22 | #90784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D116 | 2 |
| C29×C22⋊Q8 | 2 |
| C2×#90784 | 2 |
| C22⋊#6597 | 2 |
| #11745157 | 2 |
| #450 | 29 |