Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
458 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22590060 | C2 | semidirect |
| 5. #22586442 | C2 | semidirect |
| 6. #22586441 | C2 | semidirect |
| 7. C71×#2141 | C2 | semidirect |
| 14. #17986254 | C4 | semidirect |
| 167. #2141 | D71 | semidirect |
| 171. C71 | #13075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601442 | 2 |
| #22597991 | 2 |
| #22590060 | 2 |
| #22588383 | 2 |
| #22586442 | 2 |
| #22586441 | 2 |
| C71×#2141 | 2 |
| #13075 | 71 |