Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
486 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22586955 | C2 | semidirect |
| 5. #22586240 | C2 | semidirect |
| 6. #22586196 | C2 | semidirect |
| 7. C71×#1503 | C2 | semidirect |
| 10. #17986276 | C4 | semidirect |
| 11. #17986276 | C4 | semidirect |
| 12. #17986201 | C4 | semidirect |
| 13. #17986201 | C4 | semidirect |
| 215. #1503 | D71 | semidirect |
| 218. C71 | #9165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598435 | 2 |
| #22597374 | 2 |
| #22588168 | 2 |
| #22586955 | 2 |
| #22586240 | 2 |
| #22586196 | 2 |
| C71×#1503 | 2 |
| #9165 | 71 |