Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
239 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 36 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×#66359 | C2 | semidirect |
| 12. #66359 | D3 | direct (N × H) |
| 90. C22×D3 | #733 | semidirect |
| 114. C22×C3 | C2×#733 | semidirect |
| 138. D3 | #66359 | direct (N × H) |
| 141. C22 | D3×#733 | semidirect |
| 145. C3 | C2×#66359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66359 | 2 |
| C22×C3×D3×C9 | 3 |
| D3×#1094 | 3 |
| C2×#66359 | 3 |
| D3×#733 | 4 |