Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#90809 | C2 | semidirect |
| 2. C2×#90784 | C2 | semidirect |
| 3. C2×D232 | C2 | semidirect |
| 4. #11745257 | C2 | semidirect |
| 5. C29×#103 | C2 | semidirect |
| 6. #11745168 | C2 | semidirect |
| 7. #11745157 | C2 | semidirect |
| 27. Q8×C29 | D4 | semidirect |
| 37. D116 | D4 | semidirect |
| 69. #103 | D29 | semidirect |
| 72. C29 | #449 | semidirect |
| 92. Q8 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90809 | 2 |
| C2×#90784 | 2 |
| C2×D232 | 2 |
| #11745257 | 2 |
| C29×#103 | 2 |
| #11745168 | 2 |
| #11745157 | 2 |
| #449 | 29 |