Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22591521 | C2 | semidirect |
| 5. #22586206 | C2 | semidirect |
| 6. #22586206 | C2 | semidirect |
| 7. C71×#1556 | C2 | semidirect |
| 10. #17986351 | C4 | semidirect |
| 11. #17986347 | C4 | semidirect |
| 153. #1556 | D71 | semidirect |
| 158. C71 | #9430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598736 | 2 |
| #22591521 | 2 |
| #22586888 | 2 |
| #22586206 | 2 |
| C71×#1556 | 2 |
| #9430 | 71 |