Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
507 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 507 conjugacy classes of subgroups — too many to draw. Only its 245 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×C8 | D9 |
| commutator, hypocenter | C9 | C23×C8 |
| Frattini | C3×C4 | C23×D3 |
| Fitting | C22×C8×C9 | C2 |
| socle | C23×C3 | C4×D3 |
| prime radical | C23×D9 | C4 |
| cosocle | C4×C9 | C24 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C22×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C8×C9 | C2 | semidirect |
| 3. C22×C9⋊C8 | C2 | semidirect |
| 4. C2×C8×D9 | C2 | direct (N × H) |
| 11. C2×C8×C9 | C22 | semidirect |
| 12. C2×C9⋊C8 | C22 | semidirect |
| 13. C8×D9 | C22 | direct (N × H) |
| 19. C22×D9 | C8 | direct (N × H) |
| 26. C8×C9 | C23 | semidirect |
| 27. C9⋊C8 | C23 | semidirect |
| 37. C22×C9 | C2×C8 | semidirect |
| 39. C2×D9 | C2×C8 | direct (N × H) |
| 47. C22×C8 | D9 | direct (N × H) |
| 58. C2×C9 | C22×C8 | semidirect |
| 60. D9 | C22×C8 | direct (N × H) |
| 68. C2×C8 | C2×D9 | direct (N × H) |
| 76. C9 | C23×C8 | semidirect |
| 86. C8 | C22×D9 | direct (N × H) |
| 92. C22 | C8×D9 | direct (N × H) |
| 99. C2 | C2×C8×D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D9 | 2 |
| C22×C8×C9 | 2 |
| C22×C9⋊C8 | 2 |
| C2×C8×D9 | 2 |
| C22×D3×C8 | 3 |