Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#41×C29 | C2 | semidirect |
| 2. C2×#90805 | C2 | semidirect |
| 3. #11745313 | C2 | semidirect |
| 4. #11745312 | C2 | semidirect |
| 5. #11745311 | C2 | semidirect |
| 6. #11745304 | C2 | semidirect |
| 7. #11745294 | C2 | semidirect |
| 8. C2×#90777 | C2 | semidirect |
| 12. #41×C29 | C22 | semidirect |
| 13. C2×Q8×C29 | C22 | semidirect |
| 15. C2×D4×C29 | C22 | semidirect |
| 22. #90805 | C22 | semidirect |
| 23. C2×D116 | C22 | semidirect |
| 25. C2×Dic58 | C22 | semidirect |
| 26. #90785 | C22 | semidirect |
| 27. #90784 | C22 | semidirect |
| 28. #90783 | C22 | semidirect |
| 29. #90782 | C22 | semidirect |
| 30. #90777 | C22 | semidirect |
| 31. #90777 | C22 | semidirect |
| 32. C2×#6597 | C22 | semidirect |
| 83. C2×#41 | D29 | semidirect |
| 90. C29 | #575 | semidirect |
| 98. #41 | C2×D29 | semidirect |
| 100. C2×Q8 | C2×D29 | semidirect |
| 104. C2×D4 | C2×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C29 | 2 |
| C2×#90805 | 2 |
| #11745313 | 2 |
| #11745312 | 2 |
| #11745311 | 2 |
| #11745304 | 2 |
| #11745294 | 2 |
| C2×#90777 | 2 |
| #575 | 29 |