Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
330 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 330 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 |
|---|---|---|
| 15. #3756 | C4 | direct (N × H) |
| 58. C32×C4 | Q16 | semidirect |
| 102. C3×C4 | #216 | semidirect |
| 107. C32 | C4×Q16 | semidirect |
| 130. C4 | #3756 | direct (N × H) |
| 133. C3 | C4×#216 | 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×#3756 | 2 |
| C4×#634 | 2 |
| #63662 | 2 |
| #63637 | 2 |
| #63634 | 2 |
| C4×C3⋊(C3⋊C8) | 2 |
| C4×#216 | 3 |