Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22590548 | C2 | semidirect |
| 3. #22590531 | C2 | semidirect |
| 4. #22590126 | C2 | semidirect |
| 5. #22590050 | C2 | semidirect |
| 6. #22589951 | C2 | semidirect |
| 7. C2×#427×C71 | C2 | semidirect |
| 16. #17985826 | C22 | semidirect |
| 17. #17985824 | C22 | semidirect |
| 18. #17985802 | C22 | semidirect |
| 19. #17985799 | C22 | semidirect |
| 145. C2×#427 | D71 | semidirect |
| 151. C71 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597921 | 2 |
| #22590548 | 2 |
| #22590531 | 2 |
| #22590126 | 2 |
| #22590050 | 2 |
| #22589951 | 2 |
| C2×#427×C71 | 2 |
| #33647 | 71 |