Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #22596951 | C2 | semidirect |
| 2. #22590552 | C2 | semidirect |
| 3. #22590112 | C2 | semidirect |
| 4. C2×#17985812 | C2 | semidirect |
| 5. #22589961 | C2 | semidirect |
| 10. #17986048 | C22 | semidirect |
| 13. #17985821 | C22 | semidirect |
| 15. #17985781 | C22 | semidirect |
| 137. C71 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596951 | 2 |
| #22590552 | 2 |
| #22590112 | 2 |
| C2×#17985812 | 2 |
| #22589961 | 2 |
| C71×#3058 | 2 |
| #33657 | 71 |