Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
194 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 110 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×C16 | C2 | semidirect |
| 3. C2×C3×C3⋊C16 | C2 | semidirect |
| 4. C3×#798 | C2 | direct (N × H) |
| 6. C2×#798 | C3 | direct (N × H) |
| 12. C32×C16 | C22 | semidirect |
| 13. C3×C3⋊C16 | C22 | semidirect |
| 19. C2×C3×C16 | D3 | semidirect |
| 20. C2×C3×C16 | C2×C3 | semidirect |
| 21. C2×C3⋊C16 | C2×C3 | semidirect |
| 22. #798 | C2×C3 | direct (N × H) |
| 45. C3×C16 | C2×D3 | semidirect |
| 46. C3×C16 | C22×C3 | semidirect |
| 47. C3⋊C16 | C22×C3 | semidirect |
| 57. C2×C16 | C3×D3 | semidirect |
| 77. C2×C32 | M32 | semidirect |
| 86. C16 | C2×C3×D3 | semidirect |
| 102. C32 | C2×M32 | semidirect |
| 114. C2×C3 | #798 | direct (N × H) |
| 115. C2×C3 | C3×M32 | semidirect |
| 126. C3 | C2×#798 | direct (N × H) |
| 127. C3 | C2×C3×M32 | semidirect |
| 129. C2 | C3×#798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×C8 | 2 |
| C2×C32×C16 | 2 |
| C2×C3×C3⋊C16 | 2 |
| C3×#798 | 2 |
| C2×C3×M32 | 3 |
| C2×#798 | 3 |