Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 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×Q16×C29 | C2 | semidirect |
| 3. #11745306 | C2 | semidirect |
| 4. C2×#90785 | C2 | semidirect |
| 7. #11745163 | C2 | semidirect |
| 51. C2×Q16 | D29 | semidirect |
| 57. C29 | #497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×C29 | 2 |
| #11745309 | 2 |
| #11745306 | 2 |
| C2×#90785 | 2 |
| C2×#90784 | 2 |
| C2×#90773 | 2 |
| #11745163 | 2 |
| #497 | 29 |