Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
544 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22591257 | C2 | semidirect |
| 4. #22586736 | C2 | semidirect |
| 5. #22586242 | C2 | semidirect |
| 6. #22586198 | C2 | semidirect |
| 12. #17986206 | C4 | semidirect |
| 13. #17986196 | C4 | semidirect |
| 209. C71 | #9180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597808 | 2 |
| #22591257 | 2 |
| #22586835 | 2 |
| #22586736 | 2 |
| #22586242 | 2 |
| #22586198 | 2 |
| C71×#1517 | 2 |
| #9180 | 71 |