Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
182 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 55 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. C22⋊(C71⋊C32) | C2 | semidirect |
| 3. C71×C22⋊C32 | C2 | semidirect |
| 49. C22×D71 | C32 | semidirect |
| 86. C22⋊C32 | D71 | semidirect |
| 87. C71 | #7334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C2×D71)⋊C16 | 2 |
| C22⋊(C71⋊C32) | 2 |
| C71×C22⋊C32 | 2 |
| #7334 | 71 |