Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22586891 | C2 | semidirect |
| 5. #22586211 | C2 | semidirect |
| 6. #22586206 | C2 | semidirect |
| 7. C71×#1537 | C2 | semidirect |
| 9. #17986402 | C4 | semidirect |
| 10. #17986373 | C4 | semidirect |
| 11. #17986349 | C4 | semidirect |
| 12. #17986347 | C4 | semidirect |
| 162. #1537 | D71 | semidirect |
| 167. C71 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599059 | 2 |
| #22597410 | 2 |
| #22586891 | 2 |
| #22586888 | 2 |
| #22586211 | 2 |
| #22586206 | 2 |
| C71×#1537 | 2 |
| #9415 | 71 |