Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
430 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 138 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. #64289 | C2 | semidirect |
| 3. #64287 | C2 | semidirect |
| 4. #64283 | C2 | semidirect |
| 5. C2×#3787 | C2 | semidirect |
| 13. #3792 | C22 | semidirect |
| 14. C2×#622 | C22 | semidirect |
| 15. #3788 | C22 | semidirect |
| 18. #3787 | C22 | semidirect |
| 70. C3⋊D3 | #131 | semidirect |
| 92. C32 | C2×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×C3⋊D3 | 2 |
| #64289 | 2 |
| #64287 | 2 |
| #64283 | 2 |
| C2×#3787 | 2 |
| C2×#131 | 9 |