Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
516 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. C42×C71⋊C8 | C2 | semidirect |
| 4. #22587095 | C2 | semidirect |
| 5. #22586795 | C2 | semidirect |
| 7. C71×#1994 | C2 | semidirect |
| 9. #17986395 | C4 | semidirect |
| 10. #17986373 | C4 | semidirect |
| 11. #17986349 | C4 | semidirect |
| 12. #17986347 | C4 | semidirect |
| 105. C42×C71 | SD16 | semidirect |
| 141. C71⋊C8 | #104 | semidirect |
| 167. #1994 | D71 | semidirect |
| 173. C71 | #9843 | semidirect |
| 271. C42 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598900 | 2 |
| #22589168 | 2 |
| C42×C71⋊C8 | 2 |
| #22587095 | 2 |
| #22586795 | 2 |
| #22586790 | 2 |
| C71×#1994 | 2 |
| #9843 | 71 |