Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
730 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 1. #22599492 | C2 | semidirect |
| 3. #22599083 | C2 | semidirect |
| 5. #22588016 | C2 | semidirect |
| 6. #22588012 | C2 | semidirect |
| 7. #22587996 | C2 | semidirect |
| 8. #22587971 | C2 | semidirect |
| 9. #22587941 | C2 | semidirect |
| 10. #22586634 | C2 | semidirect |
| 11. C71×#1713 | C2 | semidirect |
| 184. #1713 | D71 | semidirect |
| 187. C71 | #19731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599492 | 2 |
| #22599479 | 2 |
| #22599083 | 2 |
| #22598798 | 2 |
| #22588016 | 2 |
| #22588012 | 2 |
| #22587996 | 2 |
| #22587971 | 2 |
| #22587941 | 2 |
| #22586634 | 2 |
| C71×#1713 | 2 |
| #19731 | 71 |