Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 2. C2×Q16×C29 | C2 | semidirect |
| 3. #11745308 | C2 | semidirect |
| 4. C2×#90784 | C2 | semidirect |
| 5. #11745183 | C2 | semidirect |
| 6. #11745169 | C2 | semidirect |
| 7. #11745168 | C2 | semidirect |
| 62. C2×Q16 | D29 | semidirect |
| 68. C29 | #452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90809 | 2 |
| C2×Q16×C29 | 2 |
| #11745308 | 2 |
| C2×#90784 | 2 |
| #11745183 | 2 |
| #11745169 | 2 |
| #11745168 | 2 |
| #452 | 29 |