Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
458 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #22587025 | C2 | semidirect |
| 5. #22586200 | C2 | semidirect |
| 6. #22586199 | C2 | semidirect |
| 7. C71×#1549 | C2 | semidirect |
| 191. #1549 | D71 | semidirect |
| 195. C71 | #9194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596977 | 2 |
| #22594162 | 2 |
| #22587025 | 2 |
| #22586652 | 2 |
| #22586200 | 2 |
| #22586199 | 2 |
| C71×#1549 | 2 |
| #9194 | 71 |