Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
492 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #22598887 | C2 | semidirect |
| 4. #22589184 | C2 | semidirect |
| 6. #22586231 | C2 | semidirect |
| 7. C71×#1485 | C2 | semidirect |
| 185. #1485 | D71 | semidirect |
| 187. C71 | #10116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599723 | 2 |
| #22599470 | 2 |
| #22598887 | 2 |
| #22589184 | 2 |
| #22586931 | 2 |
| #22586231 | 2 |
| C71×#1485 | 2 |
| #10116 | 71 |