Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
488 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C92 | D3 |
| commutator, hypocenter | C3 | C2×C4×C92 |
| Frattini | C2×C32 | C2×C32×D3 |
| Fitting | C3×C4×C92 | C2 |
| socle, cosocle | C2×C33 | C22×C32 |
| prime radical | C2×C32×D3 | C2×C32 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C4×C92 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C4×C92 | C2 | semidirect |
| 3. C92×Dic3 | C2 | semidirect |
| 7. D3×C92 | C4 | direct (N × H) |
| 14. C4×C92 | D3 | direct (N × H) |
| 15. C3×C92 | C2×C4 | semidirect |
| 18. C4×D3×C9 | C9 | direct (N × H) |
| 32. C3×C4×C9 | C2×C9 | semidirect |
| 34. C9×Dic3 | C2×C9 | semidirect |
| 37. C92 | C4×D3 | direct (N × H) |
| 48. D3×C9 | C4×C9 | direct (N × H) |
| 59. C4×C9 | D3×C9 | direct (N × H) |
| 63. C3×C9 | C2×C4×C9 | semidirect |
| 66. C4×D3 | C92 | direct (N × H) |
| 79. C3×C4 | C2×C92 | semidirect |
| 81. Dic3 | C2×C92 | semidirect |
| 86. C9 | C4×D3×C9 | direct (N × H) |
| 92. D3 | C4×C92 | direct (N × H) |
| 95. C4 | D3×C92 | direct (N × H) |
| 97. C3 | C2×C4×C92 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C92 | 2 |
| C3×C4×C92 | 2 |
| C92×Dic3 | 2 |
| C3×C4×D3×C9 | 3 |
| C2×C4×C92 | 3 |