Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
368 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92199 |
| commutator, hypocenter | #6857 | C2×C4 |
| Frattini | C2×C33 | C2×C3⋊D3 |
| Fitting | C22×#6857 | C2 |
| socle | C22×C32 | #272 |
| prime radical | C22×C3×H(3,𝔽3) | D3 |
| cosocle | C2×#6857 | C22 |
| LCS | G ▷ #6857 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11757322 | C2 | direct (N × H) |
| 6. C2×#6857 | C4 | semidirect |
| 14. #6857 | C2×C4 | semidirect |
| 21. C2×C3×3−1+2 | Dic3 | semidirect |
| 25. C2×C32⋊C9 | Dic3 | semidirect |
| 39. C3×3−1+2 | C2×Dic3 | semidirect |
| 41. C32⋊C9 | C2×Dic3 | semidirect |
| 147. C2 | #11757322 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6857 | 2 |
| #11757322 | 2 |
| C2×C3⋊(3−1+2⋊C4) | 3 |
| C2×C3⋊((C3⋊Dic3)⋊C3) | 3 |
| C2×#66316 | 3 |