Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
100 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 35 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×#90785 | C2 | semidirect |
| 5. C29×#101 | C2 | semidirect |
| 6. #11745172 | C2 | semidirect |
| 7. #11745170 | C2 | semidirect |
| 56. #101 | D29 | semidirect |
| 57. C29 | #473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90785 | 2 |
| #11745304 | 2 |
| #11745271 | 2 |
| #11745269 | 2 |
| C29×#101 | 2 |
| #11745172 | 2 |
| #11745170 | 2 |
| #473 | 29 |