Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
470 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22597425 | C2 | semidirect |
| 5. #22586237 | C2 | semidirect |
| 6. #22586198 | C2 | semidirect |
| 7. C71×#1805 | C2 | semidirect |
| 11. #17986209 | C4 | semidirect |
| 12. #17986199 | C4 | semidirect |
| 186. #1805 | D71 | semidirect |
| 191. C71 | #9310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597812 | 2 |
| #22597425 | 2 |
| #22586899 | 2 |
| #22586738 | 2 |
| #22586237 | 2 |
| #22586198 | 2 |
| C71×#1805 | 2 |
| #9310 | 71 |