Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
206 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 3. #63769 | C2 | direct (N × H) |
| 8. C2×C32×C8 | C4 | semidirect |
| 9. C2×C3⋊(C3⋊C8) | C4 | semidirect |
| 10. C8×C3⋊D3 | C4 | semidirect |
| 22. C32×C8 | C2×C4 | semidirect |
| 23. C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 52. C2×C32 | #107 | semidirect |
| 54. C3⋊D3 | #107 | semidirect |
| 62. C2×C8 | #157 | semidirect |
| 74. C32 | C2×#107 | semidirect |
| 85. C8 | C2×#157 | semidirect |
| 105. C2 | #63769 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#157 | 2 |
| C2×C8×C3⋊D3 | 2 |
| #63769 | 2 |
| C2×#107 | 9 |