Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22587012 | C2 | semidirect |
| 5. #22586198 | C2 | semidirect |
| 6. #22586171 | C2 | semidirect |
| 7. C71×#1960 | C2 | semidirect |
| 10. #17986402 | C4 | semidirect |
| 11. #17986347 | C4 | semidirect |
| 184. #1960 | D71 | semidirect |
| 189. C71 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599461 | 2 |
| #22597059 | 2 |
| #22587012 | 2 |
| #22586899 | 2 |
| #22586198 | 2 |
| #22586171 | 2 |
| C71×#1960 | 2 |
| #9291 | 71 |