Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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. C22×Q8×C29 | C2 | semidirect |
| 3. C2×#90785 | C2 | semidirect |
| 4. #11745304 | C2 | direct (N × H) |
| 5. C2×#90784 | C2 | semidirect |
| 6. C2×#90777 | C2 | semidirect |
| 10. C2×Q8×C29 | C22 | semidirect |
| 19. #90785 | C22 | semidirect |
| 20. #90784 | C22 | semidirect |
| 21. #90777 | C22 | semidirect |
| 54. C2×C29 | #137 | semidirect |
| 58. C22×Q8 | D29 | semidirect |
| 63. C29 | C2×#137 | semidirect |
| 70. C2×Q8 | C2×D29 | semidirect |
| 111. C2 | #11745304 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×C29 | 2 |
| C2×#90805 | 2 |
| C2×#90785 | 2 |
| #11745304 | 2 |
| C2×#90784 | 2 |
| C2×#90777 | 2 |
| C2×#137 | 29 |