Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
430 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22587057 | C2 | semidirect |
| 5. #22586210 | C2 | semidirect |
| 6. #22586196 | C2 | semidirect |
| 7. C71×#1987 | C2 | semidirect |
| 9. #17986391 | C4 | semidirect |
| 10. #17986367 | C4 | semidirect |
| 192. #1987 | D71 | semidirect |
| 197. C71 | #9376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599367 | 2 |
| #22597476 | 2 |
| #22587057 | 2 |
| #22586863 | 2 |
| #22586210 | 2 |
| #22586196 | 2 |
| C71×#1987 | 2 |
| #9376 | 71 |