Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
516 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22589318 | C2 | semidirect |
| 4. C4×C8×Dic71 | C2 | semidirect |
| 5. #22587095 | C2 | semidirect |
| 7. C71×#1493 | C2 | semidirect |
| 9. #17986395 | C4 | semidirect |
| 10. #17986373 | C4 | semidirect |
| 11. #17986349 | C4 | semidirect |
| 12. #17986347 | C4 | semidirect |
| 88. C4×Dic71 | SD16 | semidirect |
| 141. C71⋊C8 | #104 | semidirect |
| 171. #1493 | D71 | semidirect |
| 173. C71 | #9843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598900 | 2 |
| #22589318 | 2 |
| #22589167 | 2 |
| C4×C8×Dic71 | 2 |
| #22587095 | 2 |
| #22586792 | 2 |
| C71×#1493 | 2 |
| #9843 | 71 |