Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
450 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22586852 | C2 | semidirect |
| 5. #22586234 | C2 | semidirect |
| 6. #22586212 | C2 | semidirect |
| 7. C71×#1526 | C2 | semidirect |
| 10. #17986291 | C4 | semidirect |
| 11. #17986286 | C4 | semidirect |
| 12. #17986206 | C4 | semidirect |
| 13. #17986201 | C4 | semidirect |
| 198. #1526 | D71 | semidirect |
| 202. C71 | #9160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598496 | 2 |
| #22597358 | 2 |
| #22588153 | 2 |
| #22586852 | 2 |
| #22586234 | 2 |
| #22586212 | 2 |
| C71×#1526 | 2 |
| #9160 | 71 |