Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
366 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 127 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. C4×#634 | C2 | semidirect |
| 5. #63637 | C2 | semidirect |
| 6. #63635 | C2 | semidirect |
| 7. C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 15. #3754 | C4 | direct (N × H) |
| 39. #634 | C2×C4 | semidirect |
| 41. C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 61. C32×C4 | SD16 | semidirect |
| 109. C3×C4 | #214 | semidirect |
| 114. C32 | C4×SD16 | semidirect |
| 141. C4 | #3754 | direct (N × H) |
| 144. C3 | C4×#214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D4 | 2 |
| C2×#3754 | 2 |
| C4×#634 | 2 |
| #63659 | 2 |
| #63637 | 2 |
| #63635 | 2 |
| C4×C3⋊(C3⋊C8) | 2 |
| C4×#214 | 3 |