Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22589061 | C2 | semidirect |
| 4. #22586839 | C2 | semidirect |
| 6. #22586170 | C2 | semidirect |
| 7. C71×#1542 | C2 | semidirect |
| 191. #1542 | D71 | semidirect |
| 196. C71 | #10547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598688 | 2 |
| #22589061 | 2 |
| #22586990 | 2 |
| #22586839 | 2 |
| #22586836 | 2 |
| #22586170 | 2 |
| C71×#1542 | 2 |
| #10547 | 71 |