Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
840 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 211 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×Q8×C3⋊D3 | C2 | semidirect |
| 2. C32×C4⋊Q8 | C2 | semidirect |
| 3. #64155 | C2 | semidirect |
| 4. #64105 | C2 | semidirect |
| 6. #64097 | C2 | semidirect |
| 8. C4×#634 | C2 | semidirect |
| 28. C3×C4⋊Q8 | D3 | semidirect |
| 44. C4⋊(C3⋊D3) | Q8 | semidirect |
| 48. #634 | D4 | semidirect |
| 70. C2×C3⋊D3 | C2×Q8 | semidirect |
| 74. C32×C4 | C2×Q8 | semidirect |
| 80. C4⋊Q8 | C3⋊D3 | semidirect |
| 128. C3×C4 | D3×Q8 | semidirect |
| 132. C32 | D4×Q8 | semidirect |
| 161. C4 | Q8×C3⋊D3 | semidirect |
| 162. C3 | #5727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊D3 | 2 |
| C32×C4⋊Q8 | 2 |
| #64155 | 2 |
| #64105 | 2 |
| #64102 | 2 |
| #64097 | 2 |
| C4×C4⋊(C3⋊D3) | 2 |
| C4×#634 | 2 |
| #5727 | 3 |