Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
334 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Dic3×#731 | C2 | direct (N × H) |
| 3. C2×Dic3×3−1+2 | C3 | semidirect |
| 5. C2×C3×C9×Dic3 | C3 | semidirect |
| 7. C2×C3×#731 | C4 | semidirect |
| 12. Dic3×3−1+2 | C2×C3 | semidirect |
| 14. C3×C9×Dic3 | C2×C3 | semidirect |
| 20. C3×#731 | C2×C4 | semidirect |
| 28. C2×C3×3−1+2 | C3×C4 | semidirect |
| 32. C2×C32×C9 | C3×C4 | semidirect |
| 40. C2×#731 | Dic3 | direct (N × H) |
| 62. C3×3−1+2 | C2×C3×C4 | semidirect |
| 64. C32×C9 | C2×C3×C4 | semidirect |
| 68. #731 | C2×Dic3 | direct (N × H) |
| 84. C2×3−1+2 | C3×Dic3 | semidirect |
| 100. C2×C3×C9 | C3×Dic3 | semidirect |
| 126. 3−1+2 | C2×C3×Dic3 | semidirect |
| 134. C3×C9 | C2×C3×Dic3 | semidirect |
| 138. C2×Dic3 | #731 | direct (N × H) |
| 175. Dic3 | C2×#731 | direct (N × H) |
| 200. C2×C3 | C4×#731 | semidirect |
| 211. C3 | C2×C4×#731 | semidirect |
| 213. C2 | Dic3×#731 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#731 | 2 |
| Dic3×#731 | 2 |
| C2×Dic3×3−1+2 | 3 |
| C2×Dic3×H(3,𝔽3) | 3 |
| C2×C3×C9×Dic3 | 3 |
| C2×C4×#731 | 3 |