Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
687 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 687 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 1. C22×C32⋊H(3,𝔽3) | C2 | semidirect |
| 2. C2×(C3⋊D3)⋊H(3,𝔽3) | C2 | semidirect |
| 3. (C3⋊Dic3)⋊H(3,𝔽3) | C2 | semidirect |
| 4. C32×#638 | C3 | semidirect |
| 6. C3×#638⋊C3 | C3 | semidirect |
| 10. C22×C34 | C2×C3 | semidirect |
| 11. C2×C32×C3⋊D3 | C2×C3 | semidirect |
| 12. C32×C3⋊Dic3 | C2×C3 | semidirect |
| 15. C22×C3×H(3,𝔽3) | D3 | semidirect |
| 16. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 18. C2×C3×(C3⋊D3)⋊C3 | C2×C3 | semidirect |
| 20. C3×(C3⋊Dic3)⋊C3 | C2×C3 | semidirect |
| 21. C32⋊H(3,𝔽3) | D4 | semidirect |
| 50. C22×C33 | C3×D3 | semidirect |
| 73. C34 | C3×D4 | semidirect |
| 76. C3×H(3,𝔽3) | #67 | semidirect |
| 77. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 80. #638 | H(3,𝔽3) | semidirect |
| 150. C22×C32 | (C3⋊D3)⋊C3 | semidirect |
| 151. C22×C32 | C2×H(3,𝔽3) | semidirect |
| 153. C2×C3⋊D3 | C2×H(3,𝔽3) | semidirect |
| 161. C3⋊Dic3 | C2×H(3,𝔽3) | semidirect |
| 175. C33 | C3×#67 | semidirect |
| 286. C32 | #638⋊C3 | semidirect |
| 287. C32 | D4×H(3,𝔽3) | semidirect |
| 316. C22 | (C3⋊D3)⋊H(3,𝔽3) | semidirect |
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 |
| C2×(C3⋊D3)⋊H(3,𝔽3) | 2 |
| (C3⋊Dic3)⋊H(3,𝔽3) | 2 |
| C32×#638 | 3 |
| #67×H(3,𝔽3) | 3 |
| C3×#638⋊C3 | 3 |