Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
513 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 513 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 4. #10619881 | C2 | direct (N × H) |
| 26. C2×C3×H(3,𝔽3) | Q8 | semidirect |
| 49. C3×H(3,𝔽3) | C2×Q8 | semidirect |
| 77. C2×C33 | Dic6 | semidirect |
| 78. C2×C33 | Dic6 | semidirect |
| 83. C2×H(3,𝔽3) | Dic6 | semidirect |
| 121. C33 | C2×Dic6 | semidirect |
| 122. C33 | C2×Dic6 | semidirect |
| 124. H(3,𝔽3) | C2×Dic6 | semidirect |
| 161. C2×C32 | #627 | semidirect |
| 162. C2×C32 | #634 | semidirect |
| 198. C32 | C2×#627 | semidirect |
| 199. C32 | C2×#634 | semidirect |
| 214. C2×C3 | #6196 | semidirect |
| 227. C3 | C2×#6196 | semidirect |
| 229. C2 | #10619881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊#1084 | 2 |
| C2×C3⋊((C3⋊Dic3)⋊C3) | 2 |
| C2×C3×(C3⋊Dic3)⋊C3 | 2 |
| #10619881 | 2 |
| C2×#6296 | 3 |
| C2×#6293 | 3 |
| C2×#6196 | 3 |