Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22590114 | C2 | semidirect |
| 3. #22590087 | C2 | semidirect |
| 4. #22590067 | C2 | semidirect |
| 5. #22589951 | C2 | semidirect |
| 6. #22586454 | C2 | semidirect |
| 7. C71×#1810 | C2 | semidirect |
| 46. C2×C71⋊C16 | D4 | semidirect |
| 187. #1810 | D71 | semidirect |
| 189. C71 | #13395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597921 | 2 |
| #22590114 | 2 |
| #22590087 | 2 |
| #22590067 | 2 |
| #22589951 | 2 |
| #22586454 | 2 |
| C71×#1810 | 2 |
| #13395 | 71 |