Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
474 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D27⋊C3 |
| commutator, cosocle, hypocenter | C27 | C23×C32 |
| Frattini | C9 | C22×C32×D3 |
| Fitting | C22×C3×C27⋊C3 | C2 |
| socle | C22×C32 | C3×D9 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C22×C3 | |
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 | direct (N × H) |
| 4. C22×D27⋊C3 | C3 | direct (N × H) |
| 5. C22×C3×D27 | C3 | semidirect |
| 6. C2×C3×C27⋊C3 | C22 | semidirect |
| 7. C3×D27⋊C3 | C22 | direct (N × H) |
| 11. C22×C27⋊C3 | C2×C3 | semidirect |
| 13. C22×C3×C27 | C2×C3 | semidirect |
| 14. C2×D27⋊C3 | C2×C3 | direct (N × H) |
| 15. C2×C3×D27 | C2×C3 | semidirect |
| 16. C3×C27⋊C3 | C23 | semidirect |
| 20. C22×D27 | C32 | semidirect |
| 24. C2×C27⋊C3 | C22×C3 | semidirect |
| 26. C2×C3×C27 | C22×C3 | semidirect |
| 27. D27⋊C3 | C22×C3 | direct (N × H) |
| 28. C3×D27 | C22×C3 | semidirect |
| 39. C22×C27 | C2×C32 | semidirect |
| 40. C2×D27 | C2×C32 | semidirect |
| 43. C27⋊C3 | C23×C3 | semidirect |
| 45. C3×C27 | C23×C3 | semidirect |
| 60. C2×C27 | C22×C32 | semidirect |
| 61. D27 | C22×C32 | semidirect |
| 80. C27 | C23×C32 | semidirect |
| 99. C22×C3 | D27⋊C3 | direct (N × H) |
| 114. C2×C3 | C2×D27⋊C3 | direct (N × H) |
| 118. C22 | C3×D27⋊C3 | direct (N × H) |
| 121. C3 | C22×D27⋊C3 | direct (N × H) |
| 124. C2 | C2×C3×D27⋊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 |
| C22×C32×D9 | 3 |
| C22×D27⋊C3 | 3 |
| C22×C3×D27 | 3 |