Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#17985837 | C2 | semidirect |
| 2. #22590598 | C2 | semidirect |
| 3. D16×Dic71 | C2 | semidirect |
| 4. Dic71⋊C32 | C2 | semidirect |
| 5. #22586522 | C2 | semidirect |
| 6. #22586518 | C2 | semidirect |
| 105. C71 | #13689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985837 | 2 |
| #22590598 | 2 |
| D16×Dic71 | 2 |
| Dic71⋊C32 | 2 |
| #22586522 | 2 |
| #22586518 | 2 |
| C2×D32×C71 | 2 |
| #13689 | 71 |