Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
202 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22590198 | C2 | semidirect |
| 4. #22586541 | C2 | semidirect |
| 5. #22586522 | C2 | semidirect |
| 6. C32×Dic71 | C2 | semidirect |
| 11. #17985837 | C4 | semidirect |
| 24. Dic568 | C2×C4 | semidirect |
| 30. C71⋊C32 | C2×C4 | semidirect |
| 80. Dic71 | SD64 | semidirect |
| 93. C71 | C4×SD64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985837 | 2 |
| #22590198 | 2 |
| D16×Dic71 | 2 |
| #22586541 | 2 |
| #22586522 | 2 |
| C32×Dic71 | 2 |
| C71×#1415 | 2 |
| C4×SD64 | 71 |