Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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×#124 | C2 | semidirect |
| 2. C2×#90784 | C2 | semidirect |
| 4. C4×D116 | C2 | semidirect |
| 5. #11745183 | C2 | semidirect |
| 6. #11745180 | C2 | semidirect |
| 7. C4⋊#6597 | C2 | semidirect |
| 58. #124 | D29 | semidirect |
| 63. C29 | #463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#124 | 2 |
| C2×#90784 | 2 |
| C2×#90782 | 2 |
| C4×D116 | 2 |
| #11745183 | 2 |
| #11745180 | 2 |
| C4⋊#6597 | 2 |
| #463 | 29 |