Finite Group DatabasebetaFinite Group Databasebeta← C2×H(3,𝔽3)×C3⋊Dic3 #14518952
Order 1944.
1488 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 231 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 |
|---|---|---|
| 2. H(3,𝔽3)×C3⋊Dic3 | C2 | direct (N × H) |
| 3. C2×C32×C3⋊Dic3 | C3 | semidirect |
| 5. C2×C32×H(3,𝔽3) | C4 | semidirect |
| 8. C32×C3⋊Dic3 | C2×C3 | semidirect |
| 12. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 17. C2×C34 | C3×C4 | semidirect |
| 21. C2×C3×H(3,𝔽3) | Dic3 | semidirect |
| 35. C34 | C2×C3×C4 | semidirect |
| 37. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 39. C2×C3⋊Dic3 | H(3,𝔽3) | direct (N × H) |
| 48. C2×C33 | C3×Dic3 | semidirect |
| 56. C2×H(3,𝔽3) | C3⋊Dic3 | direct (N × H) |
| 68. C3⋊Dic3 | C2×H(3,𝔽3) | direct (N × H) |
| 74. C33 | C2×C3×Dic3 | semidirect |
| 78. H(3,𝔽3) | C2×C3⋊Dic3 | direct (N × H) |
| 94. C2×C32 | C4×H(3,𝔽3) | semidirect |
| 97. C2×C32 | C3×C3⋊Dic3 | semidirect |
| 114. C32 | C2×C4×H(3,𝔽3) | semidirect |
| 116. C32 | C2×C3×C3⋊Dic3 | semidirect |
| 124. C2×C3 | Dic3×H(3,𝔽3) | semidirect |
| 133. C3 | C2×Dic3×H(3,𝔽3) | semidirect |
| 135. C2 | H(3,𝔽3)×C3⋊Dic3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×H(3,𝔽3) | 2 |
| H(3,𝔽3)×C3⋊Dic3 | 2 |
| C2×C32×C3⋊Dic3 | 3 |
| C2×Dic3×H(3,𝔽3) | 3 |