Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
462 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 462 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 |
|---|---|---|
| 2. C2×Q32×D71 | C2 | semidirect |
| 3. #22590659 | C2 | direct (N × H) |
| 4. C2×#17985839 | C2 | semidirect |
| 5. C2×#17985838 | C2 | semidirect |
| 6. C2×#17985836 | C2 | semidirect |
| 7. C2×#17985832 | C2 | semidirect |
| 8. C2×Q64×C71 | C2 | semidirect |
| 16. Q32×D71 | C22 | semidirect |
| 20. #17985839 | C22 | semidirect |
| 21. #17985838 | C22 | semidirect |
| 22. #17985836 | C22 | semidirect |
| 23. #17985832 | C22 | semidirect |
| 27. Q64×C71 | C22 | semidirect |
| 124. C2×C71 | #2264 | semidirect |
| 132. C2×Q64 | D71 | semidirect |
| 136. C71 | C2×#2264 | semidirect |
| 151. Q64 | C2×D71 | semidirect |
| 253. C2 | #22590659 | 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×Q32×D71 | 2 |
| #22590659 | 2 |
| C2×#17985839 | 2 |
| C2×#17985838 | 2 |
| C2×#17985836 | 2 |
| C2×#17985832 | 2 |
| C2×Q64×C71 | 2 |
| C2×#2264 | 71 |