Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
474 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 142 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. Q8×#157 | C2 | semidirect |
| 3. D4×#157 | C2 | semidirect |
| 4. #64286 | C2 | semidirect |
| 5. C2×C4×#157 | C2 | semidirect |
| 7. C32×#41 | C4 | semidirect |
| 8. #3832 | C4 | semidirect |
| 10. #3830 | C4 | semidirect |
| 12. #3828 | C4 | semidirect |
| 24. C32×Q8 | C2×C4 | semidirect |
| 25. C32×D4 | C2×C4 | semidirect |
| 26. C2×C32×C4 | C2×C4 | semidirect |
| 27. #638 | C2×C4 | semidirect |
| 28. C2×C3⋊Dic3 | C2×C4 | semidirect |
| 29. C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 30. C4×C3⋊D3 | C2×C4 | semidirect |
| 31. C4×C3⋊D3 | C2×C4 | semidirect |
| 34. #634 | C2×C4 | semidirect |
| 48. #157 | #41 | direct (N × H) |
| 77. #41 | #157 | direct (N × H) |
| 95. C32 | C4×#41 | semidirect |
| 98. Q8 | C2×#157 | semidirect |
| 101. D4 | C2×#157 | semidirect |
| 110. C2×C4 | C2×#157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×C3⋊D3 | 2 |
| Q8×#157 | 2 |
| D4×#157 | 2 |
| #64286 | 2 |
| C2×C4×#157 | 2 |
| C4×#41 | 9 |