Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
894 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 231 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. C22×C32×D4 | C2 | semidirect |
| 2. C2×#3828 | C2 | semidirect |
| 3. C2×#3754 | C2 | semidirect |
| 4. #64141 | C2 | direct (N × H) |
| 5. C2×#3753 | C2 | semidirect |
| 6. C2×#3748 | C2 | semidirect |
| 12. C2×C32×D4 | C22 | semidirect |
| 16. #3828 | C22 | semidirect |
| 17. C2×C4⋊(C3⋊D3) | C22 | semidirect |
| 19. C2×#634 | C22 | semidirect |
| 20. #3754 | C22 | semidirect |
| 21. #3753 | C22 | semidirect |
| 22. #3748 | C22 | semidirect |
| 23. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 24. C22×C3×D4 | D3 | semidirect |
| 45. C4⋊(C3⋊D3) | C23 | semidirect |
| 48. #634 | C23 | semidirect |
| 49. C3⋊(C3⋊C8) | C23 | semidirect |
| 55. C2×C3×D4 | C2×D3 | semidirect |
| 80. C22×D4 | C3⋊D3 | semidirect |
| 107. C2×C32 | AGL(1,ℤ/8) | semidirect |
| 119. C2×D4 | C2×C3⋊D3 | semidirect |
| 138. C32 | C2×AGL(1,ℤ/8) | semidirect |
| 161. C2×C3 | #932 | semidirect |
| 176. C3 | C2×#932 | semidirect |
| 180. C2 | #64141 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D4 | 2 |
| C2×#3828 | 2 |
| C2×#3754 | 2 |
| #64141 | 2 |
| C2×#3753 | 2 |
| C2×#3748 | 2 |
| C2×#932 | 3 |