Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
966 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 966 conjugacy classes of subgroups — too many to draw. Only its 287 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. #64155 | C2 | direct (N × H) |
| 5. C2×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 6. C2×#3750 | C2 | semidirect |
| 10. C2×C32×Q8 | C22 | semidirect |
| 18. C4⋊(C3⋊Dic3) | C22 | semidirect |
| 19. #3750 | C22 | semidirect |
| 20. C22×C3×Q8 | D3 | semidirect |
| 29. C22×C3⋊D3 | Q8 | semidirect |
| 44. C2×C3×Q8 | C2×D3 | semidirect |
| 61. C2×C3⋊D3 | C2×Q8 | semidirect |
| 66. C22×Q8 | C3⋊D3 | semidirect |
| 87. C2×C32 | C22⋊Q8 | semidirect |
| 94. C2×Q8 | C2×C3⋊D3 | semidirect |
| 116. C32 | C2×C22⋊Q8 | semidirect |
| 132. C2×C3 | #946 | semidirect |
| 149. C3 | C2×#946 | semidirect |
| 151. C2 | #64155 | 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 |
| #64155 | 2 |
| C2×#3752 | 2 |
| C2×C4⋊(C3⋊Dic3) | 2 |
| C2×#3750 | 2 |
| C2×#946 | 3 |