Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
286 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 286 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 |
| 3. C3×#924 | C2 | semidirect |
| 4. C2×C3×#204 | C2 | semidirect |
| 5. C3×#821 | C2 | semidirect |
| 6. C3×#817 | C2 | semidirect |
| 7. C3×#816 | C2 | semidirect |
| 9. #5114 | C3 | direct (N × H) |
| 25. C22×C3×C8 | D3 | semidirect |
| 26. C22×C3×C8 | C2×C3 | semidirect |
| 30. #924 | C2×C3 | semidirect |
| 31. C2×#204 | C2×C3 | semidirect |
| 35. #821 | C2×C3 | semidirect |
| 36. #817 | C2×C3 | semidirect |
| 37. #816 | C2×C3 | semidirect |
| 53. C32×C8 | D4 | semidirect |
| 87. C22×C32 | SD16 | semidirect |
| 99. C22×C8 | C3×D3 | semidirect |
| 142. C3×C8 | #67 | semidirect |
| 143. C3×C8 | C3×D4 | semidirect |
| 173. C22×C3 | #204 | semidirect |
| 174. C22×C3 | C3×SD16 | semidirect |
| 195. C32 | #465 | semidirect |
| 211. C8 | C3×#67 | semidirect |
| 231. C22 | C3×#204 | semidirect |
| 240. C3 | #5114 | direct (N × H) |
| 241. C3 | C3×#465 | 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 |
| C3×#924 | 2 |
| C2×C3×#204 | 2 |
| C3×#821 | 2 |
| C3×#817 | 2 |
| C3×#816 | 2 |
| C3×#465 | 3 |
| #5114 | 3 |