Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
308 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22586515 | C2 | semidirect |
| 4. #22586500 | C2 | semidirect |
| 12. #541×C71 | C4 | semidirect |
| 15. #494×C71 | C4 | semidirect |
| 16. #491×C71 | C4 | semidirect |
| 22. #433×C71 | C4 | semidirect |
| 148. C71 | #13608 | semidirect |
| 149. #541 | Dic71 | semidirect |
| 152. #494 | Dic71 | semidirect |
| 153. #491 | Dic71 | semidirect |
| 159. #433 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590029 | 2 |
| #22590015 | 2 |
| #22586515 | 2 |
| #22586500 | 2 |
| C71×#3223 | 2 |
| #13608 | 71 |