Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
400 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 3. #22586632 | C2 | semidirect |
| 4. #22586184 | C2 | semidirect |
| 5. C71×#1450 | C2 | semidirect |
| 111. #1450 | D71 | semidirect |
| 113. C71 | #8158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986058 | 2 |
| #22586652 | 2 |
| #22586632 | 2 |
| #22586184 | 2 |
| C71×#1450 | 2 |
| #8158 | 71 |