Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
482 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #22586787 | C2 | semidirect |
| 5. #22586233 | C2 | semidirect |
| 6. #22586196 | C2 | semidirect |
| 7. C71×#2320 | C2 | semidirect |
| 10. #17986294 | C4 | semidirect |
| 11. #17986199 | C4 | semidirect |
| 182. #2320 | D71 | semidirect |
| 188. C71 | #9330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598462 | 2 |
| #22589258 | 2 |
| #22586847 | 2 |
| #22586787 | 2 |
| #22586233 | 2 |
| #22586196 | 2 |
| C71×#2320 | 2 |
| #9330 | 71 |