Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
676 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 676 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. #22589321 | C2 | semidirect |
| 3. #22587071 | C2 | semidirect |
| 5. #22586977 | C2 | semidirect |
| 6. #22586851 | C2 | semidirect |
| 12. #17986719 | C4 | semidirect |
| 14. D4×Dic142 | C4 | semidirect |
| 214. C71 | #8496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602754 | 2 |
| #22589321 | 2 |
| #22587071 | 2 |
| #22587062 | 2 |
| #22586977 | 2 |
| #22586851 | 2 |
| C71×#1505 | 2 |
| #8496 | 71 |