Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
354 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 4. C32×#106 | C2 | semidirect |
| 5. #63645 | C2 | semidirect |
| 6. #63635 | C2 | semidirect |
| 7. #63634 | C2 | semidirect |
| 20. #3743 | C4 | semidirect |
| 24. C3×#106 | D3 | semidirect |
| 38. C32×C8 | C2×C4 | semidirect |
| 39. C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 70. #106 | C3⋊D3 | semidirect |
| 81. C3×C8 | C4×D3 | semidirect |
| 110. C32 | #428 | semidirect |
| 122. C8 | C4×C3⋊D3 | semidirect |
| 138. C3 | #4861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3743 | 2 |
| #64101 | 2 |
| C4⋊C4×C3⋊D3 | 2 |
| C32×#106 | 2 |
| #63645 | 2 |
| #63635 | 2 |
| #63634 | 2 |
| #4861 | 3 |