Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1854 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1854 conjugacy classes of subgroups — too many to draw. Only its 331 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. C2×#17985863 | C2 | semidirect |
| 3. #22586611 | C2 | semidirect |
| 4. #22586584 | C2 | semidirect |
| 6. C71×#1446 | C2 | semidirect |
| 9. C2×#14556117 | C4 | semidirect |
| 70. C4×Dic71 | C22⋊C4 | semidirect |
| 156. #1446 | D71 | semidirect |
| 159. C71 | #14662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556117 | 2 |
| C2×#17985863 | 2 |
| #22586611 | 2 |
| #22586584 | 2 |
| #22586580 | 2 |
| C71×#1446 | 2 |
| #14662 | 71 |