Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
298 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 74 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 | C9⋊#157 |
| commutator, hypocenter | C32×C9 | C22×C4 |
| Frattini | C3 | C22×C3⋊#157 |
| Fitting | C22×C32×C9 | C4 |
| socle | C22×C33 | Dic3 |
| prime radical | C22×C3×C3⋊D3 | D3 |
| cosocle | C9×C3⋊D3 | C23 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C9⋊#157 | C2 | direct (N × H) |
| 4. C22×C32×C9 | C4 | semidirect |
| 5. C2×C9×C3⋊D3 | C4 | semidirect |
| 7. C9⋊#157 | C22 | direct (N × H) |
| 11. C2×C32×C9 | C2×C4 | semidirect |
| 12. C9×C3⋊D3 | C2×C4 | semidirect |
| 24. C32×C9 | C22×C4 | semidirect |
| 40. C22×C32 | Dic9 | semidirect |
| 41. C2×C3⋊D3 | Dic9 | semidirect |
| 49. C22×C9 | #157 | semidirect |
| 59. C2×C32 | C2×Dic9 | semidirect |
| 60. C3⋊D3 | C2×Dic9 | semidirect |
| 67. C2×C9 | C2×#157 | semidirect |
| 79. C32 | C22×Dic9 | semidirect |
| 81. C9 | C22×#157 | semidirect |
| 93. C22 | C9⋊#157 | direct (N × H) |
| 100. C2 | C2×C9⋊#157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×C3⋊D3 | 2 |
| C2×C9⋊#157 | 2 |
| C22×C3⋊#157 | 3 |
| C22×Dic9 | 9 |