Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
282 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 78 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×C27⋊C3 | C2 | semidirect |
| 2. C2×C3×D27⋊C3 | C2 | semidirect |
| 3. C3×(C27⋊C3)⋊C4 | C2 | semidirect |
| 5. #6171⋊C3 | C3 | direct (N × H) |
| 6. C3×#6171 | C3 | semidirect |
| 14. C22×C27⋊C3 | C2×C3 | semidirect |
| 16. C22×C3×C27 | C2×C3 | semidirect |
| 17. C2×D27⋊C3 | C2×C3 | semidirect |
| 18. C2×C3×D27 | C2×C3 | semidirect |
| 19. (C27⋊C3)⋊C4 | C2×C3 | semidirect |
| 20. C3×Dic27 | C2×C3 | semidirect |
| 21. C3×C27⋊C3 | D4 | semidirect |
| 25. #6171 | C32 | semidirect |
| 52. C22×C27 | C2×C32 | semidirect |
| 53. C2×D27 | C2×C32 | semidirect |
| 54. Dic27 | C2×C32 | semidirect |
| 57. C27⋊C3 | C3×D4 | semidirect |
| 59. C3×C27 | C3×D4 | semidirect |
| 106. C27 | C32×D4 | semidirect |
| 132. C22×C3 | D27⋊C3 | semidirect |
| 158. C22 | C3×D27⋊C3 | semidirect |
| 162. C3 | #6171⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C27⋊C3 | 2 |
| C2×C3×D27⋊C3 | 2 |
| C3×(C27⋊C3)⋊C4 | 2 |
| C32×#611 | 3 |
| #6171⋊C3 | 3 |
| C3×#6171 | 3 |