Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
342 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 2. C2×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C32×C22⋊C8 | C2 | semidirect |
| 4. #63648 | C2 | semidirect |
| 5. #63644 | C2 | semidirect |
| 18. C3×C22⋊C8 | D3 | semidirect |
| 57. C22⋊C8 | C3⋊D3 | semidirect |
| 94. C32 | #481 | semidirect |
| 122. C3 | #4735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64139 | 2 |
| C2×C4⋊(C3⋊Dic3) | 2 |
| C32×C22⋊C8 | 2 |
| #63648 | 2 |
| #63644 | 2 |
| #4735 | 3 |