Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 163 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×#17986434 | C2 | semidirect |
| 2. C22×D1136 | C2 | semidirect |
| 3. #22598827 | C2 | semidirect |
| 4. #22597191 | C2 | semidirect |
| 5. #22590398 | C2 | semidirect |
| 6. #22590374 | C2 | semidirect |
| 7. #22590098 | C2 | semidirect |
| 8. #22590055 | C2 | semidirect |
| 9. C71×#2138 | C2 | semidirect |
| 16. C2×#14556071 | C22 | semidirect |
| 19. C2×#14556069 | C22 | semidirect |
| 22. #17986384 | C22 | semidirect |
| 23. #17986374 | C22 | semidirect |
| 25. #17986081 | C22 | semidirect |
| 28. Dic71⋊C16 | C22 | semidirect |
| 29. #17985799 | C22 | semidirect |
| 33. #358×C71 | C22 | semidirect |
| 34. #357×C71 | C22 | semidirect |
| 44. C2×D568 | D4 | semidirect |
| 190. #2138 | D71 | semidirect |
| 191. C71 | #33585 | semidirect |
| 214. #358 | C2×D71 | semidirect |
| 216. #357 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986434 | 2 |
| C22×D1136 | 2 |
| #22598827 | 2 |
| #22597191 | 2 |
| #22590398 | 2 |
| #22590374 | 2 |
| #22590098 | 2 |
| #22590055 | 2 |
| C71×#2138 | 2 |
| #33585 | 71 |