Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 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×M16×C29 | C2 | semidirect |
| 3. C2×#90772 | C2 | semidirect |
| 4. C22⋊#6597 | C2 | semidirect |
| 5. #11745168 | C2 | semidirect |
| 6. #11745162 | C2 | semidirect |
| 7. C8×Dic29 | C2 | semidirect |
| 34. C8×C29 | D4 | semidirect |
| 49. Dic29 | M16 | semidirect |
| 57. C2×M16 | D29 | semidirect |
| 63. C29 | #436 | semidirect |
| 92. C8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×C29 | 2 |
| C4×C22⋊D29 | 2 |
| C2×#90772 | 2 |
| C22⋊#6597 | 2 |
| #11745168 | 2 |
| #11745162 | 2 |
| C8×Dic29 | 2 |
| #436 | 29 |