Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
554 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 105 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. #10619894 | C2 | direct (N × H) |
| 20. C2×C3×H(3,𝔽3) | Q8 | semidirect |
| 35. C3×H(3,𝔽3) | C2×Q8 | semidirect |
| 50. C2×C33 | Dic6 | semidirect |
| 54. C2×H(3,𝔽3) | Dic6 | semidirect |
| 75. C33 | C2×Dic6 | semidirect |
| 77. H(3,𝔽3) | C2×Dic6 | semidirect |
| 98. C2×C32 | #627 | semidirect |
| 122. C32 | C2×#627 | semidirect |
| 134. C2×C3 | #6229 | semidirect |
| 145. C3 | C2×#6229 | semidirect |
| 147. C2 | #10619894 | 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×#1084 | 2 |
| C2×Dic3×H(3,𝔽3) | 2 |
| #10619894 | 2 |
| C2×C3×#627 | 3 |
| C2×#6229 | 3 |