Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
298 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 148 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. C2×#90800 | C2 | semidirect |
| 3. D29⋊M16 | C2 | direct (N × H) |
| 4. C2×#90796 | C2 | semidirect |
| 5. C2×D29⋊C8 | C2 | semidirect |
| 15. #90800 | C22 | semidirect |
| 16. C2×#6599 | C22 | semidirect |
| 17. #90796 | C22 | semidirect |
| 18. D29⋊C8 | C22 | semidirect |
| 37. #6599 | C23 | semidirect |
| 43. C2×D29 | M16 | semidirect |
| 53. C2×C29 | C2×M16 | semidirect |
| 56. D29 | C2×M16 | semidirect |
| 62. C29 | C22×M16 | semidirect |
| 111. C2 | D29⋊M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D29 | 2 |
| C2×#90800 | 2 |
| D29⋊M16 | 2 |
| C2×#90796 | 2 |
| C2×D29⋊C8 | 2 |
| C22×M16 | 29 |