Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
472 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22601478 | C2 | semidirect |
| 2. #22590654 | C2 | semidirect |
| 3. #22590652 | C2 | semidirect |
| 4. #22590650 | C2 | semidirect |
| 5. C2×D2272 | C2 | semidirect |
| 6. D32×D71 | C2 | semidirect |
| 7. #22590633 | C2 | semidirect |
| 8. C71×#2262 | C2 | semidirect |
| 12. #17986432 | C22 | semidirect |
| 13. C2×D1136 | C22 | semidirect |
| 14. D16×D71 | C22 | semidirect |
| 16. #17985836 | C22 | semidirect |
| 17. D2272 | C22 | semidirect |
| 18. D2272 | C22 | semidirect |
| 19. #17985834 | C22 | semidirect |
| 20. #17985833 | C22 | semidirect |
| 21. #17985832 | C22 | semidirect |
| 22. C32×D71 | C22 | semidirect |
| 23. #508×C71 | C22 | semidirect |
| 24. Q64×C71 | C22 | semidirect |
| 25. SD64×C71 | C22 | semidirect |
| 26. D32×C71 | C22 | semidirect |
| 27. C2×C32×C71 | C22 | semidirect |
| 111. #2262 | D71 | semidirect |
| 115. C71 | #33982 | semidirect |
| 120. #508 | C2×D71 | semidirect |
| 124. Q64 | C2×D71 | semidirect |
| 126. SD64 | C2×D71 | semidirect |
| 130. D32 | C2×D71 | semidirect |
| 134. C2×C32 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601478 | 2 |
| #22590654 | 2 |
| #22590652 | 2 |
| #22590650 | 2 |
| C2×D2272 | 2 |
| D32×D71 | 2 |
| #22590633 | 2 |
| C71×#2262 | 2 |
| #33982 | 71 |