Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
180 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 87 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. C4⋊(C71⋊C32) | C2 | semidirect |
| 5. #22586473 | C2 | semidirect |
| 6. C32×Dic71 | C2 | semidirect |
| 7. C71×C4⋊C32 | C2 | semidirect |
| 88. C4⋊C32 | D71 | semidirect |
| 93. C71 | #13641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589935 | 2 |
| C4⋊(C71⋊C32) | 2 |
| (C2×D71)⋊C32 | 2 |
| #22586473 | 2 |
| C32×Dic71 | 2 |
| C71×C4⋊C32 | 2 |
| #13641 | 71 |