Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
270 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 100. C32 | #479 | semidirect |
| 124. C3 | #5022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q8 | 2 |
| #64079 | 2 |
| #63662 | 2 |
| #63635 | 2 |
| #63634 | 2 |
| C4⋊(C3⋊(C3⋊C8)) | 2 |
| #5022 | 3 |