Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
322 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Dic58 | C2 | semidirect |
| 4. C2×C4⋊Dic29 | C2 | semidirect |
| 5. #11745286 | C2 | direct (N × H) |
| 6. C2×#90779 | C2 | semidirect |
| 15. C2×Dic58 | C22 | semidirect |
| 17. C4⋊Dic29 | C22 | semidirect |
| 18. #90779 | C22 | semidirect |
| 21. C23×C29 | Q8 | semidirect |
| 39. C22×C29 | C2×Q8 | semidirect |
| 48. C2×C29 | C22⋊Q8 | semidirect |
| 58. C29 | C2×C22⋊Q8 | semidirect |
| 73. C23 | Dic58 | semidirect |
| 90. C22 | C2×Dic58 | semidirect |
| 99. C2 | #11745286 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C29 | 2 |
| C22×Dic58 | 2 |
| C2×C22⋊Dic29 | 2 |
| C2×C4⋊Dic29 | 2 |
| #11745286 | 2 |
| C2×#90779 | 2 |
| C2×C22⋊Q8 | 29 |