Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
472 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 2. #22597358 | C2 | semidirect |
| 3. #22588153 | C2 | semidirect |
| 4. #22586848 | C2 | semidirect |
| 5. #22586234 | C2 | semidirect |
| 6. #22586212 | C2 | semidirect |
| 7. C71×#1525 | C2 | semidirect |
| 10. #17986281 | C4 | semidirect |
| 11. #17986276 | C4 | semidirect |
| 12. #17986196 | C4 | semidirect |
| 13. #17986191 | C4 | semidirect |
| 206. #1525 | D71 | semidirect |
| 210. C71 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598485 | 2 |
| #22597358 | 2 |
| #22588153 | 2 |
| #22586848 | 2 |
| #22586234 | 2 |
| #22586212 | 2 |
| C71×#1525 | 2 |
| #9162 | 71 |