Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22589320 | C2 | semidirect |
| 5. #22586814 | C2 | semidirect |
| 6. #22586234 | C2 | semidirect |
| 7. C71×#1299 | C2 | semidirect |
| 10. #17986408 | C4 | semidirect |
| 11. #17986393 | C4 | semidirect |
| 12. #17986368 | C4 | semidirect |
| 13. #17986359 | C4 | semidirect |
| 205. #1299 | D71 | semidirect |
| 206. C71 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598946 | 2 |
| #22597507 | 2 |
| #22589320 | 2 |
| #22586827 | 2 |
| #22586814 | 2 |
| #22586234 | 2 |
| C71×#1299 | 2 |
| #8998 | 71 |