Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
990 conjugacy classes of subgroups; only the 279 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 279 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. C22×C32×Q8 | C2 | semidirect |
| 3. #64156 | C2 | direct (N × H) |
| 4. C2×#3752 | C2 | semidirect |
| 5. C2×C4×C3⋊Dic3 | C2 | semidirect |
| 9. C2×C32×Q8 | C22 | semidirect |
| 15. #3752 | C22 | semidirect |
| 16. C4×C3⋊Dic3 | C22 | semidirect |
| 17. C22×C3×Q8 | D3 | semidirect |
| 37. C2×C3×Q8 | C2×D3 | semidirect |
| 54. C22×Q8 | C3⋊D3 | semidirect |
| 71. C2×C32 | #124 | semidirect |
| 77. C2×Q8 | C2×C3⋊D3 | semidirect |
| 94. C32 | C2×#124 | semidirect |
| 107. C2×C3 | #947 | semidirect |
| 120. C3 | C2×#947 | semidirect |
| 122. C2 | #64156 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q8 | 2 |
| C22×C4⋊(C3⋊D3) | 2 |
| #64156 | 2 |
| C2×#3752 | 2 |
| C2×C4×C3⋊Dic3 | 2 |
| C2×#947 | 3 |