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. C4×D4×C29 | C2 | semidirect |
| 2. C2×#90783 | C2 | semidirect |
| 4. #11745237 | C2 | semidirect |
| 5. #11745158 | C2 | semidirect |
| 6. #11745157 | C2 | semidirect |
| 7. C4⋊#6597 | C2 | semidirect |
| 59. C4×D4 | 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 |
|---|---|
| C4×D4×C29 | 2 |
| C2×#90783 | 2 |
| C2×#90782 | 2 |
| #11745237 | 2 |
| #11745158 | 2 |
| #11745157 | 2 |
| C4⋊#6597 | 2 |
| #463 | 29 |