Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
904 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 904 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 13. C32×H(3,𝔽3) | Q8 | semidirect |
| 38. C34 | Dic6 | semidirect |
| 41. C3×H(3,𝔽3) | Dic6 | semidirect |
| 77. C33 | #627 | semidirect |
| 81. H(3,𝔽3) | #634 | semidirect |
| 111. C32 | #6196 | semidirect |
| 112. C32 | #6293 | semidirect |
| 127. C3 | #10619900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊(C3⋊((C3⋊Dic3)⋊C3)) | 2 |
| C32×#1084 | 2 |
| #10620148 | 3 |
| #10619900 | 3 |