Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
334 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 1. C22×C3×#731 | C2 | semidirect |
| 2. C2×D3×#731 | C2 | semidirect |
| 3. Dic3×#731 | C2 | semidirect |
| 4. #67×3−1+2 | C3 | semidirect |
| 6. C3×C9×#67 | C3 | semidirect |
| 11. C22×C3×3−1+2 | C2×C3 | semidirect |
| 13. C22×C32×C9 | C2×C3 | semidirect |
| 14. C2×D3×3−1+2 | C2×C3 | semidirect |
| 16. C2×C3×D3×C9 | C2×C3 | semidirect |
| 17. Dic3×3−1+2 | C2×C3 | semidirect |
| 19. C3×C9×Dic3 | C2×C3 | semidirect |
| 24. C22×#731 | D3 | semidirect |
| 26. C3×#731 | D4 | semidirect |
| 61. C22×3−1+2 | C3×D3 | semidirect |
| 71. C22×C3×C9 | C3×D3 | semidirect |
| 79. C3×3−1+2 | C3×D4 | semidirect |
| 81. C32×C9 | C3×D4 | semidirect |
| 85. #731 | #67 | direct (N × H) |
| 157. 3−1+2 | C3×#67 | semidirect |
| 165. C3×C9 | C3×#67 | semidirect |
| 169. #67 | #731 | direct (N × H) |
| 211. C22×C3 | C2×#731 | semidirect |
| 213. C2×D3 | C2×#731 | semidirect |
| 217. Dic3 | C2×#731 | semidirect |
| 251. C22 | D3×#731 | semidirect |
| 258. C3 | D4×#731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#731 | 2 |
| C2×D3×#731 | 2 |
| Dic3×#731 | 2 |
| #67×3−1+2 | 3 |
| #67×H(3,𝔽3) | 3 |
| C3×C9×#67 | 3 |
| D4×#731 | 3 |