Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22597435 | C2 | semidirect |
| 5. #22586201 | C2 | semidirect |
| 6. #22586169 | C2 | semidirect |
| 7. C71×#1506 | C2 | semidirect |
| 9. #17986378 | C4 | semidirect |
| 10. #17986373 | C4 | semidirect |
| 11. #17986351 | C4 | semidirect |
| 12. #17986347 | C4 | semidirect |
| 170. #1506 | D71 | semidirect |
| 175. C71 | #9282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599292 | 2 |
| #22597435 | 2 |
| #22586847 | 2 |
| #22586808 | 2 |
| #22586201 | 2 |
| #22586169 | 2 |
| C71×#1506 | 2 |
| #9282 | 71 |