Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
416 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22588369 | C2 | semidirect |
| 3. #22586353 | C2 | semidirect |
| 4. #22586350 | C2 | semidirect |
| 5. C71×#2112 | C2 | semidirect |
| 6. C2×#14556150 | C4 | semidirect |
| 8. #17986240 | C4 | semidirect |
| 10. #17986235 | C4 | semidirect |
| 14. #17986037 | C4 | semidirect |
| 178. #2112 | D71 | semidirect |
| 182. C71 | #11890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597921 | 2 |
| #22588369 | 2 |
| #22586353 | 2 |
| #22586350 | 2 |
| C71×#2112 | 2 |
| #11890 | 71 |