Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
486 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#3743 | C2 | semidirect |
| 3. C4⋊C4×C3⋊D3 | C2 | semidirect |
| 4. C32×#103 | C2 | semidirect |
| 5. #63662 | C2 | semidirect |
| 6. #63648 | C2 | semidirect |
| 7. #63636 | C2 | semidirect |
| 11. #3832 | C4 | semidirect |
| 26. C3×#103 | D3 | semidirect |
| 33. C32×Q8 | C2×C4 | semidirect |
| 41. C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 80. #103 | C3⋊D3 | semidirect |
| 86. C3×Q8 | C4×D3 | semidirect |
| 133. C32 | #417 | semidirect |
| 137. Q8 | C4×C3⋊D3 | semidirect |
| 170. C3 | #4803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3832 | 2 |
| C2×#3743 | 2 |
| C4⋊C4×C3⋊D3 | 2 |
| C32×#103 | 2 |
| #63662 | 2 |
| #63648 | 2 |
| #63636 | 2 |
| #4803 | 3 |