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. #11745297 | C2 | semidirect |
| 4. C4×C22⋊D29 | C2 | semidirect |
| 5. C4×C22⋊D29 | C2 | semidirect |
| 6. #11745288 | C2 | semidirect |
| 7. C2×C4×Dic29 | C2 | semidirect |
| 8. #11745260 | C2 | semidirect |
| 9. #11745251 | C2 | semidirect |
| 10. #11745248 | C2 | semidirect |
| 11. #11745247 | C2 | semidirect |
| 12. #11745241 | C2 | semidirect |
| 13. #11745240 | C2 | semidirect |
| 14. #11745234 | C2 | semidirect |
| 15. C4×Dic58 | C2 | semidirect |
| 115. C4×D4 | D29 | semidirect |
| 119. 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 |
| #11745301 | 2 |
| #11745297 | 2 |
| C4×C22⋊D29 | 2 |
| #11745288 | 2 |
| C2×C4×Dic29 | 2 |
| #11745260 | 2 |
| #11745251 | 2 |
| #11745248 | 2 |
| #11745247 | 2 |
| #11745241 | 2 |
| #11745240 | 2 |
| #11745234 | 2 |
| C4×Dic58 | 2 |
| #529 | 29 |