Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
306 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 1. C22×C32×C8 | C2 | semidirect |
| 2. C3×#930 | C2 | semidirect |
| 3. C2×C3×D24 | C2 | semidirect |
| 4. C3×#821 | C2 | semidirect |
| 5. C3×#818 | C2 | semidirect |
| 7. #5115 | C3 | direct (N × H) |
| 19. C22×C3×C8 | D3 | semidirect |
| 20. C22×C3×C8 | C2×C3 | semidirect |
| 22. #930 | C2×C3 | semidirect |
| 23. C2×D24 | C2×C3 | semidirect |
| 26. #821 | C2×C3 | semidirect |
| 27. #818 | C2×C3 | semidirect |
| 39. C32×C8 | D4 | semidirect |
| 65. C22×C32 | D8 | semidirect |
| 75. C22×C8 | C3×D3 | semidirect |
| 108. C3×C8 | #67 | semidirect |
| 109. C3×C8 | C3×D4 | semidirect |
| 135. C22×C3 | D24 | semidirect |
| 136. C22×C3 | C3×D8 | semidirect |
| 153. C32 | #466 | semidirect |
| 165. C8 | C3×#67 | semidirect |
| 185. C22 | C3×D24 | semidirect |
| 192. C3 | #5115 | direct (N × H) |
| 193. C3 | C3×#466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C8 | 2 |
| C3×#930 | 2 |
| C2×C3×D24 | 2 |
| C3×#821 | 2 |
| C3×#818 | 2 |
| C3×#466 | 3 |
| #5115 | 3 |