Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
770 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 167 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. #22599083 | C2 | semidirect |
| 3. #22598883 | C2 | semidirect |
| 5. #22588016 | C2 | semidirect |
| 6. #22587973 | C2 | semidirect |
| 7. #22587961 | C2 | semidirect |
| 8. #22587956 | C2 | semidirect |
| 9. #22587926 | C2 | semidirect |
| 10. #22586644 | C2 | semidirect |
| 11. C71×#1722 | C2 | semidirect |
| 158. C71⋊C8 | #137 | semidirect |
| 183. #1722 | D71 | semidirect |
| 189. C71 | #19746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599083 | 2 |
| #22599057 | 2 |
| #22598883 | 2 |
| #22598794 | 2 |
| #22588016 | 2 |
| #22587973 | 2 |
| #22587961 | 2 |
| #22587956 | 2 |
| #22587926 | 2 |
| #22586644 | 2 |
| C71×#1722 | 2 |
| #19746 | 71 |