Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1306 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 1. #22603052 | C2 | semidirect |
| 2. #22597044 | C2 | semidirect |
| 3. #22588759 | C2 | semidirect |
| 4. #22588628 | C2 | semidirect |
| 5. #22588291 | C2 | semidirect |
| 6. #22588142 | C2 | semidirect |
| 12. C22×#11765849 | C22 | semidirect |
| 15. #17986026 | C22 | semidirect |
| 18. #17985963 | C22 | semidirect |
| 19. #17985955 | C22 | semidirect |
| 20. #17985769 | C22 | semidirect |
| 35. C2×#11765849 | D4 | semidirect |
| 39. C22×C71⋊C8 | D4 | semidirect |
| 152. C71 | #21484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22603052 | 2 |
| #22597044 | 2 |
| #22588759 | 2 |
| #22588628 | 2 |
| #22588291 | 2 |
| #22588142 | 2 |
| C71×#3025 | 2 |
| #21484 | 71 |