Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
470 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22590077 | C2 | semidirect |
| 3. #22588386 | C2 | semidirect |
| 4. #22586446 | C2 | semidirect |
| 5. C71×#3407 | C2 | semidirect |
| 8. #17986257 | C4 | semidirect |
| 9. #17986252 | C4 | semidirect |
| 50. M32×C71 | D4 | semidirect |
| 139. #3407 | D71 | semidirect |
| 144. C71 | #13077 | semidirect |
| 182. M32 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598002 | 2 |
| #22590077 | 2 |
| #22588386 | 2 |
| #22586446 | 2 |
| C71×#3407 | 2 |
| #13077 | 71 |