Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
289 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 289 conjugacy classes of subgroups — too many to draw. Only its 75 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. C4×#6908 | C2 | semidirect |
| 3. #11757584 | C2 | semidirect |
| 4. C4×#4208 | C3 | semidirect |
| 6. C4×#4178 | C3 | semidirect |
| 7. C4×#4176 | C3 | semidirect |
| 8. C4×#4174 | C3 | semidirect |
| 10. #92280 | C4 | direct (N × H) |
| 14. C4×#737 | C2×C3 | semidirect |
| 15. C32×C4×C9 | D3 | semidirect |
| 16. #66410 | C2×C3 | semidirect |
| 22. C4×#732 | C2×C3 | semidirect |
| 24. C4×#731 | C2×C3 | semidirect |
| 27. #66325 | C2×C3 | semidirect |
| 28. #66323 | C2×C3 | semidirect |
| 30. #6908 | C2×C4 | semidirect |
| 41. #4208 | C3×C4 | semidirect |
| 49. #4178 | C3×C4 | semidirect |
| 50. #4176 | C3×C4 | semidirect |
| 51. #4174 | C3×C4 | semidirect |
| 82. #737 | C2×C3×C4 | semidirect |
| 83. C32×C9 | C4×D3 | semidirect |
| 85. #732 | C2×C3×C4 | semidirect |
| 87. #731 | C2×C3×C4 | semidirect |
| 220. C4 | #92280 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92280 | 2 |
| C4×#6908 | 2 |
| #11757584 | 2 |
| C4×#4208 | 3 |
| C3×C4×D3×C9 | 3 |
| C4×#4178 | 3 |
| C4×#4176 | 3 |
| C4×#4174 | 3 |