Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 47 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. C29×#131 | C2 | semidirect |
| 3. #11745263 | C2 | semidirect |
| 4. #11745185 | C2 | semidirect |
| 5. #11745173 | C2 | semidirect |
| 6. #11745170 | C2 | semidirect |
| 7. #11745163 | C2 | semidirect |
| 14. #90785 | C4 | semidirect |
| 15. #90784 | C4 | semidirect |
| 16. #90783 | C4 | semidirect |
| 17. #90782 | C4 | semidirect |
| 54. #131 | D29 | semidirect |
| 59. C29 | #444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#131 | 2 |
| #11745312 | 2 |
| #11745263 | 2 |
| #11745185 | 2 |
| #11745173 | 2 |
| #11745170 | 2 |
| #11745163 | 2 |
| #444 | 29 |