Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
963 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 963 conjugacy classes of subgroups — too many to draw. Only its 92 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. C32×#1084 | C2 | semidirect |
| 3. C3×Dic3×H(3,𝔽3) | C2 | semidirect |
| 6. #10619890 | C3 | direct (N × H) |
| 8. C3×C3⋊#272 | C4 | semidirect |
| 11. C33×Dic3 | D3 | semidirect |
| 17. C3×#1084 | D3 | semidirect |
| 18. C3×#1084 | C2×C3 | semidirect |
| 20. Dic3×H(3,𝔽3) | C2×C3 | semidirect |
| 21. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 35. C3⋊#272 | C3×C4 | semidirect |
| 52. C32×Dic3 | C3×D3 | semidirect |
| 58. #1084 | C3×D3 | semidirect |
| 59. C34 | C4×D3 | semidirect |
| 64. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 65. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 117. C3×Dic3 | #272 | semidirect |
| 125. C33 | #624 | semidirect |
| 126. C33 | C3×C4×D3 | semidirect |
| 132. H(3,𝔽3) | C3×C4×D3 | semidirect |
| 177. Dic3 | C3×#272 | semidirect |
| 191. C32 | C4×#272 | semidirect |
| 192. C32 | C3×#624 | semidirect |
| 219. C3 | #10619890 | direct (N × H) |
| 220. C3 | C3×C4×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊#272 | 2 |
| C32×#1084 | 2 |
| C3×Dic3×H(3,𝔽3) | 2 |
| C32×#624 | 3 |
| C3×C4×#272 | 3 |
| #10619890 | 3 |