Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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. Q8×Dic29 | C2 | semidirect |
| 4. C29×#103 | C2 | semidirect |
| 6. #11745163 | C2 | semidirect |
| 7. #11745155 | C2 | semidirect |
| 13. #90784 | C4 | semidirect |
| 22. Q8×C29 | C2×C4 | semidirect |
| 33. #6597 | C2×C4 | semidirect |
| 54. #103 | D29 | semidirect |
| 57. C29 | #440 | semidirect |
| 72. Q8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic29 | 2 |
| C2×#90784 | 2 |
| #11745255 | 2 |
| C29×#103 | 2 |
| #11745169 | 2 |
| #11745163 | 2 |
| #11745155 | 2 |
| #440 | 29 |