Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
354 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 191 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 |
|---|---|---|
| 4. #63645 | C2 | semidirect |
| 5. #63644 | C2 | semidirect |
| 9. C32×M16 | C4 | semidirect |
| 31. C32×C8 | C2×C4 | semidirect |
| 35. C3×M16 | Dic3 | semidirect |
| 67. C3×C8 | C2×Dic3 | semidirect |
| 74. M16 | C3⋊Dic3 | semidirect |
| 92. C32 | #428 | semidirect |
| 102. C8 | C2×C3⋊Dic3 | semidirect |
| 117. C3 | #5121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M16 | 2 |
| #64135 | 2 |
| C2×C4⋊(C3⋊Dic3) | 2 |
| #63645 | 2 |
| #63644 | 2 |
| #5121 | 3 |