Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
327 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 63 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×#6908 | C2 | semidirect |
| 2. C2×#92280 | C2 | semidirect |
| 3. #11757584 | C2 | semidirect |
| 4. #10619984 | C3 | semidirect |
| 6. #10619649 | C3 | semidirect |
| 7. #10619645 | C3 | semidirect |
| 8. #10619641 | C3 | semidirect |
| 13. C22×#737 | C2×C3 | semidirect |
| 14. C22×C32×C9 | D3 | semidirect |
| 15. C2×#4208 | C2×C3 | semidirect |
| 17. #66410 | C2×C3 | semidirect |
| 20. C22×#732 | C2×C3 | semidirect |
| 22. C22×#731 | C2×C3 | semidirect |
| 25. C2×#4178 | C2×C3 | semidirect |
| 26. C2×#4176 | C2×C3 | semidirect |
| 27. C2×#4174 | C2×C3 | semidirect |
| 28. #66325 | C2×C3 | semidirect |
| 29. #66323 | C2×C3 | semidirect |
| 30. #66321 | C2×C3 | semidirect |
| 31. #6908 | D4 | semidirect |
| 92. #737 | C3×D4 | semidirect |
| 93. C32×C9 | #67 | semidirect |
| 95. #732 | C3×D4 | semidirect |
| 97. #731 | C3×D4 | semidirect |
| 261. C22 | #92280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6908 | 2 |
| C2×#92280 | 2 |
| #11757584 | 2 |
| #10619984 | 3 |
| C3×C9×#67 | 3 |
| #10619649 | 3 |
| #10619645 | 3 |
| #10619641 | 3 |