Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
324 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 109 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. #64078 | C2 | semidirect |
| 3. C32×C4⋊C8 | C2 | semidirect |
| 5. #63645 | C2 | semidirect |
| 18. C3×C4⋊C8 | D3 | semidirect |
| 28. C4⋊(C3⋊D3) | Q8 | semidirect |
| 55. C4⋊C8 | C3⋊D3 | semidirect |
| 91. C32 | #474 | semidirect |
| 117. C3 | #4846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊D3) | 2 |
| #64078 | 2 |
| C32×C4⋊C8 | 2 |
| #63648 | 2 |
| #63645 | 2 |
| #4846 | 3 |