Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1280 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 1280 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C3⋊D32 |
| commutator, Fitting, cosocle | C2×C32×H(3,𝔽3) | C22 |
| socle | C2×C33 | C2×C3⋊D3 |
| hypocenter | C32×H(3,𝔽3) | D4 |
| LCS | G ▷ C2×C32×H(3,𝔽3) ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3⋊(C3⋊#272) | C2 | semidirect |
| 2. C2×C3⋊D3×H(3,𝔽3) | C2 | semidirect |
| 3. C32×#1084 | C2 | semidirect |
| 10. C2×C32×C3⋊D3 | D3 | semidirect |
| 15. C3×#1084 | D3 | semidirect |
| 16. C32×H(3,𝔽3) | D4 | semidirect |
| 44. #1084 | C3⋊D3 | semidirect |
| 45. C34 | #67 | semidirect |
| 47. C3×H(3,𝔽3) | D12 | semidirect |
| 75. C2×C3⋊D3 | #272 | semidirect |
| 90. C33 | #626 | semidirect |
| 94. H(3,𝔽3) | C4⋊(C3⋊D3) | semidirect |
| 134. C32 | #6235 | semidirect |
| 136. C32 | #6292 | semidirect |
| 156. C3 | #10619892 | 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 |
| C2×C3⋊D3×H(3,𝔽3) | 2 |
| C32×#1084 | 2 |
| C3×#6292 | 3 |
| #10619892 | 3 |