Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
748 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 748 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. #22587068 | C2 | semidirect |
| 3. #22587060 | C2 | semidirect |
| 4. #22586975 | C2 | semidirect |
| 5. #22586851 | C2 | semidirect |
| 6. #22586847 | C2 | semidirect |
| 7. C71×#1963 | C2 | semidirect |
| 9. #17986710 | C4 | semidirect |
| 12. #17986669 | C4 | semidirect |
| 223. #1963 | D71 | semidirect |
| 229. C71 | #8493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602738 | 2 |
| #22587068 | 2 |
| #22587060 | 2 |
| #22586975 | 2 |
| #22586851 | 2 |
| #22586847 | 2 |
| C71×#1963 | 2 |
| #8493 | 71 |