Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 330 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 |
|---|---|---|
| 14. #3746 | C4 | semidirect |
| 44. C3⋊Dic3 | Q16 | semidirect |
| 77. C32 | C4×Q16 | semidirect |
| 97. C3 | #4873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3746 | 2 |
| #64096 | 2 |
| C32×#107 | 2 |
| C8×C3⋊Dic3 | 2 |
| #63637 | 2 |
| #4873 | 3 |