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. #22599487 | C2 | semidirect |
| 3. #22599086 | C2 | semidirect |
| 5. #22588020 | C2 | semidirect |
| 6. #22588009 | C2 | semidirect |
| 7. #22587992 | C2 | semidirect |
| 8. #22587974 | C2 | semidirect |
| 9. #22587958 | C2 | semidirect |
| 10. #22586634 | C2 | semidirect |
| 11. C71×#1708 | C2 | semidirect |
| 185. #1708 | 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 |
|---|---|
| #22599487 | 2 |
| #22599471 | 2 |
| #22599086 | 2 |
| #22598794 | 2 |
| #22588020 | 2 |
| #22588009 | 2 |
| #22587992 | 2 |
| #22587974 | 2 |
| #22587958 | 2 |
| #22586634 | 2 |
| C71×#1708 | 2 |
| #19731 | 71 |