Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
418 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 1. C2×C32×C4⋊C4 | C2 | semidirect |
| 4. C2×C3×Dic3⋊C4 | C2 | semidirect |
| 5. C3×C3⋊#95 | C2 | semidirect |
| 7. #4993 | C3 | direct (N × H) |
| 19. C2×C3×C4⋊C4 | D3 | semidirect |
| 20. C2×C3×C4⋊C4 | C2×C3 | semidirect |
| 25. C2×Dic3⋊C4 | C2×C3 | semidirect |
| 27. C3⋊#95 | C2×C3 | semidirect |
| 81. C2×C4⋊C4 | C3×D3 | semidirect |
| 173. C32 | #399 | semidirect |
| 222. C3 | #4993 | direct (N × H) |
| 223. C3 | C3×#399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4⋊C4 | 2 |
| C2×C3×(C2×D3)⋊C4 | 2 |
| C2×C3×Dic3⋊C4 | 2 |
| C3×C3⋊#95 | 2 |
| C3×#399 | 3 |
| #4993 | 3 |