Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
444 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 101 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×#3756 | C2 | semidirect |
| 3. C2×#3746 | C2 | semidirect |
| 5. C32×#103 | C2 | semidirect |
| 7. #63637 | C2 | semidirect |
| 28. C3×#103 | D3 | semidirect |
| 69. C2×C3⋊D3 | Q16 | semidirect |
| 82. #103 | C3⋊D3 | semidirect |
| 133. C32 | #451 | semidirect |
| 168. C3 | #4809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊D3 | 2 |
| C2×#3756 | 2 |
| C2×#3746 | 2 |
| #64106 | 2 |
| C32×#103 | 2 |
| #63647 | 2 |
| #63637 | 2 |
| #4809 | 3 |