Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
302 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 81 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. M64×D71 | C2 | semidirect |
| 3. #367×D71 | C2 | semidirect |
| 4. #22586528 | C2 | semidirect |
| 5. #22586527 | C2 | semidirect |
| 6. #22586526 | C2 | semidirect |
| 7. C71×#1418 | C2 | semidirect |
| 9. #17986432 | C4 | semidirect |
| 13. #17986428 | C4 | semidirect |
| 14. Q32×D71 | C4 | semidirect |
| 16. D16×D71 | C4 | semidirect |
| 19. #17985833 | C22 | semidirect |
| 22. #17985827 | C22 | semidirect |
| 25. M64×C71 | C22 | semidirect |
| 26. #367×C71 | C22 | semidirect |
| 38. Dic568 | C2×C4 | semidirect |
| 43. D1136 | C2×C4 | semidirect |
| 54. Q32×C71 | C2×C4 | semidirect |
| 56. D16×C71 | C2×C4 | semidirect |
| 146. D71 | #1418 | direct (N × H) |
| 153. #1418 | D71 | direct (N × H) |
| 154. C71 | C2×#1418 | semidirect |
| 169. M64 | C2×D71 | semidirect |
| 173. #367 | C2×D71 | semidirect |
| 188. Q32 | C4×D71 | semidirect |
| 195. D16 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D71 | 2 |
| M64×D71 | 2 |
| #367×D71 | 2 |
| #22586528 | 2 |
| #22586527 | 2 |
| #22586526 | 2 |
| C71×#1418 | 2 |
| C2×#1418 | 71 |