Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22589316 | C2 | semidirect |
| 4. #22588085 | C2 | semidirect |
| 5. #22586794 | C2 | semidirect |
| 7. C71×#1566 | C2 | semidirect |
| 10. #17986397 | C4 | semidirect |
| 11. #17986372 | C4 | semidirect |
| 12. #17986350 | C4 | semidirect |
| 13. #17986346 | C4 | semidirect |
| 94. C4×Dic71 | SD16 | semidirect |
| 169. #1566 | D71 | semidirect |
| 172. C71 | #9846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598899 | 2 |
| #22589316 | 2 |
| #22589167 | 2 |
| #22588085 | 2 |
| #22586794 | 2 |
| #22586790 | 2 |
| C71×#1566 | 2 |
| #9846 | 71 |