Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
298 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. C22×C71⋊C32 | C2 | semidirect |
| 2. #22590124 | C2 | semidirect |
| 3. #22586521 | C2 | semidirect |
| 4. #22586518 | C2 | semidirect |
| 13. #508×C71 | C4 | semidirect |
| 97. C71 | #13615 | semidirect |
| 100. #508 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C71⋊C32 | 2 |
| #22590124 | 2 |
| #22586521 | 2 |
| #22586518 | 2 |
| C2×#508×C71 | 2 |
| #13615 | 71 |