Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
251 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 251 conjugacy classes of subgroups — too many to draw. Only its 86 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. C3×#870 | C2 | semidirect |
| 5. C3×#808 | C2 | semidirect |
| 6. C3×#807 | C2 | semidirect |
| 7. C3×C4⋊(C3⋊C8) | C2 | semidirect |
| 9. #5009 | C3 | direct (N × H) |
| 25. #870 | C2×C3 | semidirect |
| 33. #808 | C2×C3 | semidirect |
| 34. #807 | C2×C3 | semidirect |
| 35. C4⋊(C3⋊C8) | C2×C3 | semidirect |
| 172. C32 | #478 | semidirect |
| 209. C3 | #5009 | direct (N × H) |
| 210. C3 | C3×#478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D4 | 2 |
| C3×#870 | 2 |
| C3×#832 | 2 |
| C3×#808 | 2 |
| C3×#807 | 2 |
| C3×C4⋊(C3⋊C8) | 2 |
| C3×#478 | 3 |
| #5009 | 3 |