Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
158 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 33. C32×C71 | Q8 | semidirect |
| 83. C71 | #13660 | semidirect |
| 109. C32 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic142 | 2 |
| C4⋊(C71⋊C32) | 2 |
| Dic71⋊C32 | 2 |
| #22586473 | 2 |
| C32×Dic71 | 2 |
| C71×#1397 | 2 |
| #13660 | 71 |