Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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×#17986432 | C2 | semidirect |
| 2. C2×D16×D71 | C2 | semidirect |
| 3. #22590654 | C2 | direct (N × H) |
| 4. C2×#17985836 | C2 | semidirect |
| 5. C2×D2272 | C2 | semidirect |
| 6. C2×#17985834 | C2 | semidirect |
| 7. C2×#17985832 | C2 | semidirect |
| 8. C2×SD64×C71 | C2 | semidirect |
| 12. #17986432 | C22 | semidirect |
| 15. C2×D1136 | C22 | semidirect |
| 18. D16×D71 | C22 | semidirect |
| 20. #17985836 | C22 | semidirect |
| 21. D2272 | C22 | semidirect |
| 22. #17985834 | C22 | semidirect |
| 23. #17985832 | C22 | semidirect |
| 24. C2×C71⋊C32 | C22 | semidirect |
| 25. C2×Q32×C71 | C22 | semidirect |
| 27. SD64×C71 | C22 | semidirect |
| 28. C2×C32×C71 | C22 | semidirect |
| 44. D1136 | C23 | semidirect |
| 49. C71⋊C32 | C23 | semidirect |
| 53. Q32×C71 | C23 | semidirect |
| 57. C32×C71 | C23 | semidirect |
| 129. C2×C71 | #2263 | semidirect |
| 138. C2×SD64 | D71 | semidirect |
| 142. C71 | C2×#2263 | semidirect |
| 147. C2×Q32 | C2×D71 | semidirect |
| 157. SD64 | C2×D71 | semidirect |
| 162. C2×C32 | C2×D71 | semidirect |
| 177. Q32 | C22×D71 | semidirect |
| 191. C32 | C22×D71 | semidirect |
| 265. C2 | #22590654 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986432 | 2 |
| C2×D16×D71 | 2 |
| #22590654 | 2 |
| C2×#17985836 | 2 |
| C2×D2272 | 2 |
| C2×#17985834 | 2 |
| C2×#17985832 | 2 |
| C2×SD64×C71 | 2 |
| C2×#2263 | 71 |