Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
342 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#17985825 | C2 | semidirect |
| 3. #22586518 | C2 | direct (N × H) |
| 7. C2×C71⋊C32 | C22 | semidirect |
| 9. #17985825 | C22 | semidirect |
| 13. C2×D16×C71 | C4 | semidirect |
| 28. D16×C71 | C2×C4 | semidirect |
| 83. C2×C71 | #1415 | semidirect |
| 91. C71 | C2×#1415 | semidirect |
| 95. C2×D16 | Dic71 | semidirect |
| 112. D16 | C2×Dic71 | semidirect |
| 169. C2 | #22586518 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C71⋊C32 | 2 |
| C2×#17985825 | 2 |
| #22586518 | 2 |
| C22×D16×C71 | 2 |
| C2×#1415 | 71 |