Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
314 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #22590112 | C2 | semidirect |
| 5. #22586443 | C2 | semidirect |
| 6. #22586424 | C2 | semidirect |
| 7. C71×#1773 | C2 | semidirect |
| 15. #17985814 | C4 | semidirect |
| 16. #17985811 | C4 | semidirect |
| 143. #1773 | D71 | semidirect |
| 146. C71 | #13140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590112 | 2 |
| #22590087 | 2 |
| #22590075 | 2 |
| #22589233 | 2 |
| #22586443 | 2 |
| #22586424 | 2 |
| C71×#1773 | 2 |
| #13140 | 71 |