Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
259 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 259 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 |
|---|---|---|
| 1. C32×C4×Q8 | C2 | semidirect |
| 2. C2×C3×#216 | C2 | semidirect |
| 5. C3×#810 | C2 | semidirect |
| 7. C3×C4⋊(C3⋊C8) | C2 | semidirect |
| 9. #5028 | C3 | direct (N × H) |
| 27. C3×C4×Q8 | D3 | semidirect |
| 28. C3×C4×Q8 | C2×C3 | semidirect |
| 29. C2×#216 | C2×C3 | semidirect |
| 35. #810 | C2×C3 | semidirect |
| 37. C4⋊(C3⋊C8) | C2×C3 | semidirect |
| 99. C4×Q8 | C3×D3 | semidirect |
| 186. C32 | #464 | semidirect |
| 225. C3 | #5028 | direct (N × H) |
| 226. C3 | C3×#464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q8 | 2 |
| C2×C3×#216 | 2 |
| C2×C3×#215 | 2 |
| C3×#875 | 2 |
| C3×#810 | 2 |
| C3×#809 | 2 |
| C3×C4⋊(C3⋊C8) | 2 |
| C3×#464 | 3 |
| #5028 | 3 |