Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1212 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11758091 |
| commutator, Fitting, cosocle | C2×C32×H(3,𝔽3) | C22 |
| Frattini | C2×C3 | C3⋊#1113 |
| socle | C2×C33 | D32 |
| hypocenter | C32×H(3,𝔽3) | D4 |
| LCS | G ▷ C2×C32×H(3,𝔽3) ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3⋊(C3⋊((C3⋊D3)⋊C3)) | C2 | semidirect |
| 2. C32×#1084 | C2 | semidirect |
| 7. C2×C3⋊(C3⋊(C3⋊D3)) | D3 | semidirect |
| 13. C3×#1084 | D3 | semidirect |
| 14. C32×H(3,𝔽3) | D4 | semidirect |
| 41. #1084 | C3⋊D3 | semidirect |
| 43. C34 | #67 | semidirect |
| 46. C3×H(3,𝔽3) | D12 | semidirect |
| 90. C33 | #626 | semidirect |
| 94. H(3,𝔽3) | C4⋊(C3⋊D3) | semidirect |
| 132. C32 | #6198 | semidirect |
| 133. C32 | #6292 | semidirect |
| 153. C3 | #10619902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(C3⋊((C3⋊D3)⋊C3)) | 2 |
| C32×#1084 | 2 |
| #10620147 | 3 |
| #10619902 | 3 |