Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
426 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22597441 | C2 | semidirect |
| 3. #22586934 | C2 | semidirect |
| 6. #22586177 | C2 | semidirect |
| 7. C71×#1278 | C2 | semidirect |
| 186. #1278 | D71 | semidirect |
| 187. C71 | #9070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598663 | 2 |
| #22597441 | 2 |
| #22586934 | 2 |
| #22586758 | 2 |
| #22586756 | 2 |
| #22586177 | 2 |
| C71×#1278 | 2 |
| #9070 | 71 |