Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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×M16×C29 | C2 | semidirect |
| 3. #11745288 | C2 | semidirect |
| 4. #11745173 | C2 | semidirect |
| 9. #90805 | C4 | semidirect |
| 11. C2×D116 | C4 | semidirect |
| 13. C2×Dic58 | C4 | semidirect |
| 15. M16×C29 | C22 | semidirect |
| 19. C4×Dic29 | C22 | semidirect |
| 58. C2×M16 | D29 | semidirect |
| 61. C29 | #421 | semidirect |
| 72. M16 | C2×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90805 | 2 |
| C2×M16×C29 | 2 |
| #11745288 | 2 |
| #11745173 | 2 |
| #421 | 29 |