Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
574 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 138 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×C22⋊#157 | C2 | semidirect |
| 3. D4×#157 | C2 | semidirect |
| 4. #64286 | C2 | semidirect |
| 6. C22×#157 | C22 | semidirect |
| 7. C2×C32×D4 | C4 | semidirect |
| 8. C2×#638 | C4 | semidirect |
| 9. D4×C3⋊D3 | C4 | semidirect |
| 11. C2×C4⋊(C3⋊D3) | C4 | semidirect |
| 14. C22⋊#157 | C22 | semidirect |
| 15. C4⋊#157 | C22 | semidirect |
| 16. C4×#157 | C22 | semidirect |
| 18. C23×C32 | C2×C4 | semidirect |
| 20. C22×C3⋊D3 | C2×C4 | semidirect |
| 21. C22×C3⋊D3 | C2×C4 | semidirect |
| 26. C32×D4 | C2×C4 | semidirect |
| 27. C2×C32×C4 | C2×C4 | semidirect |
| 28. #638 | C2×C4 | semidirect |
| 29. C2×C3⋊Dic3 | C2×C4 | semidirect |
| 30. C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 31. C4×C3⋊D3 | C2×C4 | semidirect |
| 82. C2×D4 | #157 | semidirect |
| 101. C32 | #518 | semidirect |
| 107. C23 | C2×#157 | semidirect |
| 110. D4 | C2×#157 | semidirect |
| 116. C2×C4 | C2×#157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C3⋊D3 | 2 |
| C2×C22⋊#157 | 2 |
| D4×#157 | 2 |
| #64286 | 2 |
| #518 | 9 |