Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
430 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 140 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×#3792 | C2 | semidirect |
| 3. C22×#622 | C2 | semidirect |
| 4. #64287 | C2 | direct (N × H) |
| 5. C2×#3788 | C2 | semidirect |
| 6. C2×#3787 | C2 | semidirect |
| 14. #3792 | C22 | semidirect |
| 18. C2×#622 | C22 | semidirect |
| 19. #3788 | C22 | semidirect |
| 20. #3787 | C22 | semidirect |
| 73. C2×C32 | #131 | semidirect |
| 99. C32 | C2×#131 | semidirect |
| 131. C2 | #64287 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3830 | 2 |
| C2×#3792 | 2 |
| C22×#622 | 2 |
| #64287 | 2 |
| C2×#3788 | 2 |
| C2×#3787 | 2 |
| C2×#131 | 9 |