Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 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. #22590557 | C2 | semidirect |
| 3. #22590513 | C2 | semidirect |
| 4. #22590418 | C2 | semidirect |
| 6. #22590229 | C2 | semidirect |
| 7. #22590156 | C2 | semidirect |
| 8. C71×#3177 | C2 | semidirect |
| 18. #17985821 | C22 | semidirect |
| 19. #17985820 | C22 | semidirect |
| 20. #17985815 | C22 | semidirect |
| 23. #17985777 | C22 | semidirect |
| 25. #499×C71 | C22 | semidirect |
| 26. #494×C71 | C22 | semidirect |
| 30. #441×C71 | C22 | semidirect |
| 161. #3177 | D71 | semidirect |
| 169. C71 | #33693 | semidirect |
| 174. #499 | C2×D71 | semidirect |
| 175. #494 | C2×D71 | semidirect |
| 183. #441 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597244 | 2 |
| #22590557 | 2 |
| #22590513 | 2 |
| #22590418 | 2 |
| #22590290 | 2 |
| #22590229 | 2 |
| #22590156 | 2 |
| C71×#3177 | 2 |
| #33693 | 71 |