Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
624 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 288 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C32×C4 | C33 |
| commutator | C32 | C2×C33×C4 |
| Frattini, cosocle | C2×C32 | C22×C33 |
| socle | C22×C32 | C2×C33 |
| prime radical | C22×C3×H(3,𝔽3) | C2×C3 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C2×C32×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#6893 | C2 | direct (N × H) |
| 3. C2×C3×C4×3−1+2 | C3 | semidirect |
| 5. C2×C32×C4×C9 | C3 | semidirect |
| 6. C2×C4×C32⋊C9 | C3 | semidirect |
| 7. C2×#6893 | C4 | direct (N × H) |
| 12. C3×C4×3−1+2 | C2×C3 | semidirect |
| 14. C32×C4×C9 | C2×C3 | semidirect |
| 16. C4×C32⋊C9 | C2×C3 | semidirect |
| 17. #6893 | C2×C4 | direct (N × H) |
| 25. C2×C3×3−1+2 | C3×C4 | semidirect |
| 29. C2×C32×C9 | C3×C4 | semidirect |
| 31. C2×C32⋊C9 | C3×C4 | semidirect |
| 47. C3×3−1+2 | C2×C3×C4 | semidirect |
| 49. C32×C9 | C2×C3×C4 | semidirect |
| 50. C32⋊C9 | C2×C3×C4 | semidirect |
| 126. C2×C4 | #6893 | direct (N × H) |
| 136. C4 | C2×#6893 | direct (N × H) |
| 141. C2 | C4×#6893 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6893 | 2 |
| C4×#6893 | 2 |
| C2×C3×C4×3−1+2 | 3 |
| C2×C3×C4×H(3,𝔽3) | 3 |
| C2×C32×C4×C9 | 3 |
| C2×C4×C32⋊C9 | 3 |