Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 2. #64153 | C2 | semidirect |
| 3. C2×#3756 | C2 | semidirect |
| 6. C2×#3746 | C2 | semidirect |
| 7. #63642 | C2 | semidirect |
| 116. C32 | #497 | semidirect |
| 145. C3 | #5167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×SD16 | 2 |
| #64153 | 2 |
| C2×#3756 | 2 |
| #64145 | 2 |
| C2×#3754 | 2 |
| C2×#3746 | 2 |
| #63642 | 2 |
| #5167 | 3 |