Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 2. C2×#17986037 | C2 | semidirect |
| 3. #22590549 | C2 | semidirect |
| 4. #22590532 | C2 | semidirect |
| 5. #22590128 | C2 | semidirect |
| 6. #22590053 | C2 | semidirect |
| 7. C71×#2112 | C2 | semidirect |
| 20. #17985827 | C22 | semidirect |
| 21. #17985825 | C22 | semidirect |
| 22. #17985804 | C22 | semidirect |
| 23. #17985801 | C22 | semidirect |
| 150. #2112 | D71 | semidirect |
| 151. C71 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597921 | 2 |
| C2×#17986037 | 2 |
| #22590549 | 2 |
| #22590532 | 2 |
| #22590128 | 2 |
| #22590053 | 2 |
| C71×#2112 | 2 |
| #33647 | 71 |