Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
177 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 177 conjugacy classes of subgroups — too many to draw. Only its 39 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. C3×#41⋊C9 | C2 | semidirect |
| 2. C3⋊(#41⋊C9) | C2 | semidirect |
| 6. C3×Q8⋊C9 | C22 | semidirect |
| 14. #41⋊C9 | D3 | semidirect |
| 18. #1009 | C9 | semidirect |
| 30. Q8⋊C9 | C2×D3 | semidirect |
| 127. C3 | #63700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#41⋊C9 | 2 |
| C3⋊(#41⋊C9) | 2 |
| C3×#1009 | 3 |
| #63700 | 3 |
| C9×Dic6 | 4 |