Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1068 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2×C3 | C3⋊D32 |
| commutator, Fitting, cosocle | C2×H(5,𝔽3) | C22 |
| hypocenter | H(5,𝔽3) | D4 |
| LCS | G ▷ C2×H(5,𝔽3) ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#92404 | C2 | semidirect |
| 2. C2×#92392 | C2 | semidirect |
| 3. #11758013 | C2 | semidirect |
| 12. C2×C3×#272 | D3 | semidirect |
| 14. C3×#1084 | D3 | semidirect |
| 16. H(5,𝔽3) | D4 | semidirect |
| 38. C2×#272 | C3⋊D3 | semidirect |
| 40. #1084 | C3⋊D3 | semidirect |
| 42. C3×H(3,𝔽3) | D12 | semidirect |
| 43. C3×H(3,𝔽3) | #67 | semidirect |
| 76. C33 | #626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92404 | 2 |
| C2×#92392 | 2 |
| #11758013 | 2 |
| #10619893 | 3 |
| #10619892 | 3 |