Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
544 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22597057 | C2 | semidirect |
| 3. #22589137 | C2 | semidirect |
| 4. #22586990 | C2 | semidirect |
| 5. #22586764 | C2 | semidirect |
| 6. #22586184 | C2 | semidirect |
| 7. C71×#1301 | C2 | semidirect |
| 102. C2×C71⋊C8 | D8 | semidirect |
| 213. #1301 | D71 | semidirect |
| 215. C71 | #9049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598341 | 2 |
| #22597057 | 2 |
| #22589137 | 2 |
| #22586990 | 2 |
| #22586764 | 2 |
| #22586184 | 2 |
| C71×#1301 | 2 |
| #9049 | 71 |