Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
356 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 356 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 |
|---|---|---|
| 2. #22589113 | C2 | semidirect |
| 5. #22586630 | C2 | semidirect |
| 6. #22586181 | C2 | semidirect |
| 7. C71×#1303 | C2 | semidirect |
| 16. #17985744 | C4 | semidirect |
| 17. #17985744 | C4 | semidirect |
| 18. #17985742 | C4 | semidirect |
| 19. #17985742 | C4 | semidirect |
| 175. #1303 | D71 | semidirect |
| 177. C71 | #9592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589258 | 2 |
| #22589113 | 2 |
| #22586987 | 2 |
| #22586790 | 2 |
| #22586630 | 2 |
| #22586181 | 2 |
| C71×#1303 | 2 |
| #9592 | 71 |