Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
318 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 144 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. #63554 | C2 | semidirect |
| 5. Dic3×C3⋊C8 | C2 | semidirect |
| 10. #3748 | C4 | semidirect |
| 15. C3×#208 | C4 | semidirect |
| 36. C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 37. C3×C3⋊C8 | C2×C4 | semidirect |
| 55. #208 | Dic3 | direct (N × H) |
| 67. C3×Dic3 | M16 | semidirect |
| 98. C3⋊C8 | C2×Dic3 | semidirect |
| 132. Dic3 | #208 | direct (N × H) |
| 133. C32 | C4×M16 | semidirect |
| 162. C3 | C4×#208 | semidirect |
| 163. C3 | Dic3×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3748 | 2 |
| C2×C3×C4×Dic3 | 2 |
| C2×C3×#208 | 2 |
| #63554 | 2 |
| Dic3×C3⋊C8 | 2 |
| Dic3×M16 | 3 |
| C4×#208 | 3 |