Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#90773 | C2 | semidirect |
| 2. C2×#90772 | C2 | semidirect |
| 3. #11745259 | C2 | semidirect |
| 5. C29×#107 | C2 | semidirect |
| 6. #11745158 | C2 | semidirect |
| 7. #11745157 | C2 | semidirect |
| 35. C8×C29 | D4 | semidirect |
| 60. #107 | D29 | semidirect |
| 63. C29 | #468 | semidirect |
| 92. C8 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90773 | 2 |
| C2×#90772 | 2 |
| #11745259 | 2 |
| #11745257 | 2 |
| C29×#107 | 2 |
| #11745158 | 2 |
| #11745157 | 2 |
| #468 | 29 |