Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
748 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 748 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 |
|---|---|---|
| 1. C2×#17986435 | C2 | semidirect |
| 2. #22598821 | C2 | semidirect |
| 3. #22597192 | C2 | semidirect |
| 4. #22590393 | C2 | semidirect |
| 5. #22590373 | C2 | semidirect |
| 6. #22590098 | C2 | semidirect |
| 7. #22590056 | C2 | semidirect |
| 8. #22590048 | C2 | semidirect |
| 9. C22×D16×C71 | C2 | semidirect |
| 15. C2×#14556072 | C22 | semidirect |
| 16. C2×#14556069 | C22 | semidirect |
| 19. #17986382 | C22 | semidirect |
| 20. #17986374 | C22 | semidirect |
| 22. D8×Dic71 | C22 | semidirect |
| 26. Dic71⋊C16 | C22 | semidirect |
| 27. #17985804 | C22 | semidirect |
| 28. #17985801 | C22 | semidirect |
| 29. #17985800 | C22 | semidirect |
| 70. C2×D8×C71 | D4 | semidirect |
| 183. C22×D16 | D71 | semidirect |
| 191. C71 | #33585 | semidirect |
| 233. C2×D8 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986435 | 2 |
| #22598821 | 2 |
| #22597192 | 2 |
| #22590393 | 2 |
| #22590373 | 2 |
| #22590098 | 2 |
| #22590056 | 2 |
| #22590048 | 2 |
| C22×D16×C71 | 2 |
| #33585 | 71 |