Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
642 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 207 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. #22597256 | C2 | semidirect |
| 3. #22590225 | C2 | semidirect |
| 4. #22590220 | C2 | semidirect |
| 5. C2×#17985805 | C2 | semidirect |
| 6. #22589939 | C2 | semidirect |
| 7. C71×#2161 | C2 | semidirect |
| 10. #17986442 | C4 | semidirect |
| 11. #17986437 | C4 | semidirect |
| 15. #17986115 | C22 | semidirect |
| 18. #17985805 | C22 | semidirect |
| 19. #17985805 | C22 | semidirect |
| 20. #17985774 | C22 | semidirect |
| 21. C16×Dic71 | C22 | semidirect |
| 24. #368×C71 | C22 | semidirect |
| 125. #2161 | D71 | semidirect |
| 128. C71 | #33464 | semidirect |
| 141. #368 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601476 | 2 |
| #22597256 | 2 |
| #22590225 | 2 |
| #22590220 | 2 |
| C2×#17985805 | 2 |
| #22589939 | 2 |
| C71×#2161 | 2 |
| #33464 | 71 |