Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
554 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 112 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. C3×C3⋊#95 | C2 | semidirect |
| 4. #63579 | C2 | semidirect |
| 10. C2×C4×C3⋊D3 | C4 | semidirect |
| 18. C3⋊#95 | D3 | semidirect |
| 124. C32 | #381 | semidirect |
| 161. C3 | #4664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C3⋊D3 | 2 |
| C2×#3722 | 2 |
| C3×C3⋊#95 | 2 |
| #63579 | 2 |
| #4664 | 3 |