Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
330 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 4. C3×#815 | C2 | semidirect |
| 5. #63554 | C2 | semidirect |
| 11. C8×C3⋊D3 | C4 | semidirect |
| 15. #3710 | C4 | semidirect |
| 22. #815 | D3 | semidirect |
| 31. C32×C8 | C2×C4 | semidirect |
| 32. C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 33. C3×C3⋊C8 | C2×C4 | semidirect |
| 77. C3×C8 | C4×D3 | semidirect |
| 80. C3⋊C8 | C4×D3 | semidirect |
| 83. C3⋊D3 | #97 | semidirect |
| 107. C32 | C2×#97 | semidirect |
| 117. C8 | #624 | semidirect |
| 132. C3 | D3×#97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊D3 | 2 |
| C4×#624 | 2 |
| C2×#3710 | 2 |
| C3×#815 | 2 |
| #63554 | 2 |
| D3×#97 | 3 |