Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
179 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 179 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | #4185 |
| commutator, hypocenter | #6879 | C2×C4 |
| Frattini | C2×C3×C9 | C2×C3⋊D3 |
| Fitting | C4×#6879 | C2 |
| socle | C2×C3 | C2×#4185 |
| prime radical | C2×#92216 | C2 |
| cosocle | C2×#6879 | C22 |
| LCS | G ▷ #6879 | |
| UCS | C1 ◁ C3×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#6879 | C2 | semidirect |
| 3. #11757339 | C2 | semidirect |
| 7. #92216 | C4 | direct (N × H) |
| 10. C4×#732 | D3 | semidirect |
| 11. C4×C92 | D3 | semidirect |
| 14. #6879 | C2×C4 | semidirect |
| 31. #732 | C4×D3 | semidirect |
| 32. C92 | C4×D3 | semidirect |
| 94. C4 | #92216 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92216 | 2 |
| C4×#6879 | 2 |
| #11757339 | 2 |
| C4×#4178 | 3 |
| C4×C9×D9 | 3 |