Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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×#90805 | C2 | semidirect |
| 2. C2×M16×C29 | C2 | semidirect |
| 3. #11745271 | C2 | semidirect |
| 4. #11745270 | C2 | semidirect |
| 5. #11745266 | C2 | semidirect |
| 11. #90805 | C22 | semidirect |
| 12. C2×D116 | C22 | semidirect |
| 14. C2×Dic58 | C22 | semidirect |
| 15. M16×C29 | C22 | semidirect |
| 16. C2×C8×C29 | C22 | semidirect |
| 17. Dic116 | C22 | semidirect |
| 18. D232 | C22 | semidirect |
| 19. #90773 | C22 | semidirect |
| 54. C2×M16 | D29 | semidirect |
| 55. C29 | #575 | semidirect |
| 68. M16 | C2×D29 | semidirect |
| 69. C2×C8 | C2×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90805 | 2 |
| C2×M16×C29 | 2 |
| #11745271 | 2 |
| #11745270 | 2 |
| #11745266 | 2 |
| #575 | 29 |