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. #22588151 | C2 | semidirect |
| 4. #22586931 | C2 | semidirect |
| 5. #22586847 | C2 | semidirect |
| 6. #22586211 | C2 | semidirect |
| 7. C71×#1300 | C2 | semidirect |
| 11. #17986285 | C4 | semidirect |
| 12. #17986280 | C4 | semidirect |
| 13. #17986200 | C4 | semidirect |
| 14. #17986195 | C4 | semidirect |
| 208. #1300 | 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 |
|---|---|
| #22598492 | 2 |
| #22597358 | 2 |
| #22588151 | 2 |
| #22586931 | 2 |
| #22586847 | 2 |
| #22586211 | 2 |
| C71×#1300 | 2 |
| #9162 | 71 |