Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
414 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 134 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×C32×M16 | C2 | semidirect |
| 3. C2×C3×#208 | C2 | semidirect |
| 4. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 6. #5126 | C3 | direct (N × H) |
| 15. C2×C32×C8 | C22 | semidirect |
| 17. C2×C3×C3⋊C8 | C22 | semidirect |
| 22. C2×C3×M16 | D3 | semidirect |
| 23. C2×C3×M16 | C2×C3 | semidirect |
| 24. C2×#208 | C2×C3 | semidirect |
| 26. (C2×D3)⋊C8 | C2×C3 | semidirect |
| 64. C2×C3×C8 | C2×D3 | semidirect |
| 65. C2×C3×C8 | C22×C3 | semidirect |
| 67. C2×C3⋊C8 | C22×C3 | semidirect |
| 74. C2×C3×D3 | M16 | semidirect |
| 81. C2×M16 | C3×D3 | semidirect |
| 133. C2×C8 | C2×C3×D3 | semidirect |
| 150. C2×D3 | C3×M16 | semidirect |
| 162. C32 | #407 | semidirect |
| 201. C3 | #5126 | direct (N × H) |
| 202. C3 | C3×#407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×D3 | 2 |
| C2×C32×M16 | 2 |
| C2×C3×#208 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#407 | 3 |
| #5126 | 3 |