Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 142 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 |
|---|---|---|
| 1. C2×SD16×C29 | C2 | semidirect |
| 2. #11745306 | C2 | semidirect |
| 3. C2×#90784 | C2 | semidirect |
| 5. C2×#90783 | C2 | semidirect |
| 6. C2×#90773 | C2 | semidirect |
| 7. C8×Dic29 | C2 | semidirect |
| 36. C8×C29 | D4 | semidirect |
| 37. #6597 | D4 | semidirect |
| 47. Dic29 | SD16 | semidirect |
| 56. C2×SD16 | D29 | semidirect |
| 60. C29 | #492 | semidirect |
| 90. C8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×C29 | 2 |
| #11745306 | 2 |
| C2×#90784 | 2 |
| #11745302 | 2 |
| C2×#90783 | 2 |
| C2×#90773 | 2 |
| C8×Dic29 | 2 |
| #492 | 29 |