Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
312 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 90 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×C32×C27 | C2 | semidirect |
| 2. C2×C32×D27 | C2 | semidirect |
| 3. C32×Dic27 | C2 | semidirect |
| 5. C3×#6171 | C3 | direct (N × H) |
| 13. C22×C3×C27 | C2×C3 | semidirect |
| 14. C2×C3×D27 | C2×C3 | semidirect |
| 15. C3×Dic27 | C2×C3 | semidirect |
| 16. C32×C27 | D4 | semidirect |
| 19. #6171 | C32 | direct (N × H) |
| 36. C22×C27 | C2×C32 | semidirect |
| 37. C2×D27 | C2×C32 | semidirect |
| 38. Dic27 | C2×C32 | semidirect |
| 41. C3×C27 | C3×D4 | semidirect |
| 60. C22×C32 | D27 | semidirect |
| 73. C27 | C32×D4 | semidirect |
| 91. C22×C3 | C3×D27 | semidirect |
| 97. C32 | #6171 | direct (N × H) |
| 111. C22 | C32×D27 | semidirect |
| 114. C3 | C3×#6171 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C27 | 2 |
| C2×C32×D27 | 2 |
| C32×Dic27 | 2 |
| C32×#611 | 3 |
| C3×#6171 | 3 |