Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
570 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 191 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. #64135 | C2 | semidirect |
| 3. C2×#3748 | C2 | semidirect |
| 4. #63659 | C2 | semidirect |
| 9. C2×C32×D4 | C4 | semidirect |
| 13. C4⋊(C3⋊Dic3) | C22 | semidirect |
| 16. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 38. C2×C3×D4 | Dic3 | semidirect |
| 80. C2×D4 | C3⋊Dic3 | semidirect |
| 98. C32 | #418 | semidirect |
| 126. C3 | #5215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D4 | 2 |
| #64135 | 2 |
| C2×#3748 | 2 |
| #63659 | 2 |
| #5215 | 3 |