Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
804 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 804 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 8. #17986729 | C4 | semidirect |
| 123. Dic142 | #103 | semidirect |
| 152. C71 | #8451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986729 | 2 |
| #22589143 | 2 |
| #22588346 | 2 |
| C2×#17985729 | 2 |
| C2×#333×C71 | 2 |
| #8451 | 71 |