Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
884 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #157⋊D3 |
| commutator, cosocle | C3×C3⋊D3 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C35 | D4 |
| hypocenter | C33 | C32×D4 |
| LCS | G ▷ C3×C3⋊D3 ▷ C33 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#1113 | C2 | semidirect |
| 2. C33×#157 | C2 | semidirect |
| 3. C3×#157⋊D3 | C3 | direct (N × H) |
| 7. C3×#1113 | C2×C3 | semidirect |
| 11. C32×#157 | D3 | semidirect |
| 12. C32×#157 | C2×C3 | semidirect |
| 13. C35 | D4 | semidirect |
| 14. #157⋊D3 | C32 | direct (N × H) |
| 29. #1113 | C2×C32 | semidirect |
| 33. C3×#157 | C3×D3 | semidirect |
| 34. C3×#157 | C2×C32 | semidirect |
| 41. C34 | D12 | semidirect |
| 42. C34 | C3×D4 | semidirect |
| 71. #157 | C32×D3 | semidirect |
| 92. C33 | C3×D12 | semidirect |
| 93. C33 | C32×D4 | semidirect |
| 94. C33 | GO+(4,𝔽2) | semidirect |
| 140. C32 | C32×D12 | semidirect |
| 141. C32 | C3×GO+(4,𝔽2) | semidirect |
| 142. C32 | #157⋊D3 | direct (N × H) |
| 161. C3 | C32×GO+(4,𝔽2) | semidirect |
| 162. C3 | C3×#157⋊D3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#1113 | 2 |
| C33×#157 | 2 |
| C3×#157⋊D3 | 3 |
| C32×GO+(4,𝔽2) | 3 |
| C32×D12 | 9 |