Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
630 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 630 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 |
|---|---|---|
| 2. #22589333 | C2 | semidirect |
| 3. #22587071 | C2 | semidirect |
| 5. #22586762 | C2 | semidirect |
| 6. #22586697 | C2 | semidirect |
| 243. C71 | #8485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602943 | 2 |
| #22589333 | 2 |
| #22587071 | 2 |
| #22586805 | 2 |
| #22586762 | 2 |
| #22586697 | 2 |
| C71×#1529 | 2 |
| #8485 | 71 |