Finite Group DatabasebetaFinite Group Databasebeta← C2×(C3⋊Dic3)⋊H(3,𝔽3) #14517422
Order 1944.
687 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 687 conjugacy classes of subgroups — too many to draw. Only its 106 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. (C3⋊Dic3)⋊H(3,𝔽3) | C2 | direct (N × H) |
| 3. C2×C32×C3⋊Dic3 | C3 | semidirect |
| 5. C2×C3×(C3⋊Dic3)⋊C3 | C3 | semidirect |
| 6. C2×C32⋊H(3,𝔽3) | C4 | semidirect |
| 9. C32×C3⋊Dic3 | C2×C3 | semidirect |
| 15. C3×(C3⋊Dic3)⋊C3 | C2×C3 | semidirect |
| 16. C32⋊H(3,𝔽3) | C2×C4 | semidirect |
| 24. C2×C34 | C3×C4 | semidirect |
| 30. C2×C3×H(3,𝔽3) | Dic3 | semidirect |
| 31. C2×C3×H(3,𝔽3) | C3×C4 | semidirect |
| 58. C34 | C2×C3×C4 | semidirect |
| 61. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 62. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 65. C2×C3⋊Dic3 | H(3,𝔽3) | semidirect |
| 86. C2×C33 | C3×Dic3 | semidirect |
| 131. C3⋊Dic3 | C2×H(3,𝔽3) | semidirect |
| 145. C33 | C2×C3×Dic3 | semidirect |
| 201. C2×C32 | (C3⋊Dic3)⋊C3 | semidirect |
| 202. C2×C32 | C4×H(3,𝔽3) | semidirect |
| 243. C32 | C2×(C3⋊Dic3)⋊C3 | semidirect |
| 244. C32 | C2×C4×H(3,𝔽3) | semidirect |
| 279. C2 | (C3⋊Dic3)⋊H(3,𝔽3) | 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 |
| (C3⋊Dic3)⋊H(3,𝔽3) | 2 |
| C2×C32×C3⋊Dic3 | 3 |
| C2×Dic3×H(3,𝔽3) | 3 |
| C2×C3×(C3⋊Dic3)⋊C3 | 3 |