Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
282 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 28. C3⋊(C3⋊C8) | Q8 | semidirect |
| 77. C32 | #446 | semidirect |
| 97. C3 | #4831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#634 | 2 |
| C32×C4⋊C8 | 2 |
| #63642 | 2 |
| #63641 | 2 |
| C4×C3⋊(C3⋊C8) | 2 |
| #4831 | 3 |