Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 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×D8×C29 | C2 | semidirect |
| 2. #11745302 | C2 | semidirect |
| 3. #11745298 | C2 | semidirect |
| 4. C2×#90783 | C2 | semidirect |
| 5. C2×#90782 | C2 | semidirect |
| 6. C2×#90773 | C2 | semidirect |
| 7. #11745163 | C2 | semidirect |
| 36. C8×C29 | D4 | semidirect |
| 37. #6597 | D4 | semidirect |
| 58. C2×D8 | D29 | semidirect |
| 62. C29 | #496 | 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×D8×C29 | 2 |
| #11745302 | 2 |
| #11745298 | 2 |
| C2×#90783 | 2 |
| C2×#90782 | 2 |
| C2×#90773 | 2 |
| #11745163 | 2 |
| #496 | 29 |