Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
426 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 3. C32×#97 | C2 | semidirect |
| 4. C8×C3⋊Dic3 | C2 | semidirect |
| 5. #63630 | C2 | semidirect |
| 14. #3743 | C4 | semidirect |
| 17. C3×#97 | D3 | semidirect |
| 27. C32×C8 | C2×C4 | semidirect |
| 28. C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 44. C3⋊Dic3 | M16 | semidirect |
| 48. #97 | C3⋊D3 | semidirect |
| 57. C3×C8 | C4×D3 | semidirect |
| 77. C32 | C4×M16 | semidirect |
| 86. C8 | C4×C3⋊D3 | semidirect |
| 97. C3 | #4707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3743 | 2 |
| C42×C3⋊D3 | 2 |
| C32×#97 | 2 |
| C8×C3⋊Dic3 | 2 |
| #63630 | 2 |
| #4707 | 3 |