Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 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×C8×D29 | C2 | semidirect |
| 4. C22⋊#6597 | C2 | semidirect |
| 5. #11745168 | C2 | semidirect |
| 6. #11745163 | C2 | semidirect |
| 7. #11745162 | C2 | semidirect |
| 34. C8×C29 | D4 | semidirect |
| 43. C2×D29 | M16 | semidirect |
| 56. C2×M16 | D29 | semidirect |
| 63. C29 | #435 | 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×C8×D29 | 2 |
| C22⋊#6597 | 2 |
| #11745168 | 2 |
| #11745163 | 2 |
| #11745162 | 2 |
| #435 | 29 |