Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
798 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 191 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×#3832 | C2 | semidirect |
| 2. C2×C32×Q16 | C2 | semidirect |
| 3. C2×#3755 | C2 | semidirect |
| 4. #64128 | C2 | direct (N × H) |
| 5. C2×#3745 | C2 | semidirect |
| 6. C2×C8×C3⋊D3 | C2 | semidirect |
| 10. #3832 | C22 | semidirect |
| 15. C32×Q16 | C22 | semidirect |
| 17. #3755 | C22 | semidirect |
| 19. #3745 | C22 | semidirect |
| 20. C8×C3⋊D3 | C22 | semidirect |
| 22. C2×C3×Q16 | D3 | semidirect |
| 50. C3×Q16 | C2×D3 | semidirect |
| 67. C2×Q16 | C3⋊D3 | semidirect |
| 86. C2×C32 | #135 | semidirect |
| 97. Q16 | C2×C3⋊D3 | semidirect |
| 112. C32 | C2×#135 | semidirect |
| 128. C2×C3 | #919 | semidirect |
| 141. C3 | C2×#919 | semidirect |
| 144. C2 | #64128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3832 | 2 |
| C2×C32×Q16 | 2 |
| C2×#3755 | 2 |
| #64128 | 2 |
| C2×#3745 | 2 |
| C2×C8×C3⋊D3 | 2 |
| C2×#919 | 3 |