Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
401 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 401 conjugacy classes of subgroups — too many to draw. Only its 90 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×#214 | C2 | semidirect |
| 3. C2×C3×#204 | C2 | semidirect |
| 4. C3×#897 | C2 | semidirect |
| 5. C32×#102 | C2 | semidirect |
| 6. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C3×#809 | C2 | semidirect |
| 9. #4776 | C3 | direct (N × H) |
| 17. C2×C3×Dic6 | C22 | semidirect |
| 18. C2×C32×C8 | C22 | semidirect |
| 19. C32×C4⋊C4 | C22 | semidirect |
| 23. C2×C3×C3⋊C8 | C22 | semidirect |
| 30. C2×#214 | C2×C3 | semidirect |
| 31. C2×#204 | C2×C3 | semidirect |
| 32. #897 | C2×C3 | semidirect |
| 35. C3×#102 | D3 | semidirect |
| 36. C3×#102 | C2×C3 | semidirect |
| 38. (C2×D3)⋊C8 | C2×C3 | semidirect |
| 39. #809 | C2×C3 | semidirect |
| 78. C2×Dic6 | C22×C3 | semidirect |
| 83. C2×C3×C8 | C2×D3 | semidirect |
| 84. C2×C3×C8 | C22×C3 | semidirect |
| 87. C3×C4⋊C4 | C2×D3 | semidirect |
| 88. C3×C4⋊C4 | C22×C3 | semidirect |
| 93. C2×C3⋊C8 | C22×C3 | semidirect |
| 105. C2×C3×D3 | SD16 | semidirect |
| 116. #102 | C3×D3 | semidirect |
| 183. C2×C8 | C2×C3×D3 | semidirect |
| 185. C4⋊C4 | C2×C3×D3 | semidirect |
| 212. C2×D3 | C3×SD16 | semidirect |
| 226. C32 | #450 | semidirect |
| 281. C3 | #4776 | direct (N × H) |
| 282. C3 | C3×#450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×D4 | 2 |
| C2×C3×#214 | 2 |
| C2×C3×#204 | 2 |
| C3×#897 | 2 |
| C32×#102 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#809 | 2 |
| C3×#450 | 3 |
| #4776 | 3 |