Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
269 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 269 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 2. C2×C3×#208 | C2 | semidirect |
| 3. C2×C3×ΓL(1,𝔽25) | C2 | semidirect |
| 4. C32×C22⋊C8 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C3×Dic3⋊C8 | C2 | semidirect |
| 7. C3×C8×Dic3 | C2 | semidirect |
| 9. #4729 | C3 | direct (N × H) |
| 27. C2×#208 | C2×C3 | semidirect |
| 28. C2×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 32. C3×C22⋊C8 | D3 | semidirect |
| 33. C3×C22⋊C8 | C2×C3 | semidirect |
| 35. (C2×D3)⋊C8 | C2×C3 | semidirect |
| 36. Dic3⋊C8 | C2×C3 | semidirect |
| 37. C8×Dic3 | C2×C3 | semidirect |
| 53. C3×C3⋊C8 | D4 | semidirect |
| 96. C3×Dic3 | M16 | semidirect |
| 102. C22⋊C8 | C3×D3 | semidirect |
| 142. C3⋊C8 | C3×D4 | semidirect |
| 193. Dic3 | C3×M16 | semidirect |
| 194. C32 | #436 | semidirect |
| 239. C3 | #4729 | direct (N × H) |
| 240. C3 | C3×#436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#67 | 2 |
| C2×C3×#208 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C32×C22⋊C8 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×Dic3⋊C8 | 2 |
| C3×C8×Dic3 | 2 |
| C3×#436 | 3 |
| #4729 | 3 |