Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
| 3. #11745298 | C2 | semidirect |
| 4. C4×C22⋊D29 | C2 | semidirect |
| 5. #11745288 | C2 | semidirect |
| 6. #11745259 | C2 | semidirect |
| 7. #11745252 | C2 | semidirect |
| 8. #11745245 | C2 | semidirect |
| 9. #11745241 | C2 | semidirect |
| 10. C42×D29 | C2 | semidirect |
| 11. C4×Dic58 | C2 | semidirect |
| 83. C4×D4 | D29 | semidirect |
| 86. C29 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×C29 | 2 |
| #11745300 | 2 |
| #11745298 | 2 |
| C4×C22⋊D29 | 2 |
| #11745288 | 2 |
| #11745259 | 2 |
| #11745252 | 2 |
| #11745245 | 2 |
| #11745241 | 2 |
| C42×D29 | 2 |
| C4×Dic58 | 2 |
| #529 | 29 |