Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
474 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 135 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. #22589969 | C2 | semidirect |
| 3. #22589961 | C2 | semidirect |
| 4. #22586421 | C2 | semidirect |
| 5. C71×#3407 | C2 | semidirect |
| 52. M32×C71 | D4 | semidirect |
| 143. #3407 | D71 | semidirect |
| 148. C71 | #12982 | semidirect |
| 189. M32 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597050 | 2 |
| #22589969 | 2 |
| #22589961 | 2 |
| #22586421 | 2 |
| C71×#3407 | 2 |
| #12982 | 71 |