Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
342 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C2×#3746 | C2 | semidirect |
| 4. C32×#107 | C2 | semidirect |
| 5. #63637 | C2 | semidirect |
| 19. C3×#107 | D3 | semidirect |
| 45. C2×C3⋊D3 | Q16 | semidirect |
| 54. #107 | C3⋊D3 | semidirect |
| 89. C32 | #467 | semidirect |
| 114. C3 | #4887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3746 | 2 |
| C2×C8×C3⋊D3 | 2 |
| #64106 | 2 |
| C32×#107 | 2 |
| #63637 | 2 |
| #4887 | 3 |