Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
290 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 92 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×C3×D3×C8 | C2 | semidirect |
| 3. C8×C3⋊Dic3 | C2 | semidirect |
| 4. #63572 | C2 | semidirect |
| 5. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 18. C2×D3×C8 | D3 | semidirect |
| 31. #625 | C8 | direct (N × H) |
| 32. C32×C8 | D4 | semidirect |
| 55. C2×C3×D3 | C2×C8 | semidirect |
| 59. C3⋊Dic3 | C2×C8 | semidirect |
| 83. C3×C8 | #67 | semidirect |
| 107. C2×D3 | D3×C8 | semidirect |
| 118. C32 | C8×D4 | semidirect |
| 129. C8 | #625 | direct (N × H) |
| 148. C3 | C8×#67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×C8 | 2 |
| C4×#625 | 2 |
| C8×C3⋊Dic3 | 2 |
| #63572 | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| C8×#67 | 3 |