Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
312 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22587128 | C2 | semidirect |
| 5. #22586231 | C2 | semidirect |
| 6. #22586177 | C2 | semidirect |
| 7. C71×#1450 | C2 | semidirect |
| 153. #1450 | D71 | semidirect |
| 156. C71 | #9586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22587128 | 2 |
| #22587000 | 2 |
| #22586792 | 2 |
| #22586756 | 2 |
| #22586231 | 2 |
| #22586177 | 2 |
| C71×#1450 | 2 |
| #9586 | 71 |