Finite Group DatabasebetaFinite Group DatabasebetaOrder 972.
118 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×D27 |
| commutator, cosocle, hypocenter | C3×C27 | C22×C3 |
| Frattini | C9 | C3×D32 |
| Fitting | C32×C27 | C22 |
| socle | C33 | C2×D9 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C3⋊D27 | C2 | semidirect |
| 2. C3×D3×C27 | C2 | semidirect |
| 3. C32×D27 | C2 | semidirect |
| 6. D3×D27 | C3 | direct (N × H) |
| 7. C32×C27 | C22 | semidirect |
| 12. C3⋊D27 | C2×C3 | semidirect |
| 14. D3×C27 | C2×C3 | semidirect |
| 18. C3×D27 | D3 | direct (N × H) |
| 19. C3×D27 | C2×C3 | semidirect |
| 29. C3×C27 | C2×D3 | semidirect |
| 30. C3×C27 | C22×C3 | semidirect |
| 47. D27 | C3×D3 | direct (N × H) |
| 62. C27 | C2×C3×D3 | semidirect |
| 73. C3×D3 | D27 | direct (N × H) |
| 87. C32 | C2×D27 | semidirect |
| 105. D3 | C3×D27 | direct (N × H) |
| 111. C3 | D3×D27 | direct (N × H) |
| 112. C3 | C2×C3×D27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C3⋊D27 | 2 |
| C3×D3×C27 | 2 |
| C32×D27 | 2 |
| C3×D3×D9 | 3 |
| C2×C3×D27 | 3 |
| D3×D27 | 3 |