Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
250 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 82 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×C32×Q16 | C2 | semidirect |
| 4. C3×#835 | C2 | semidirect |
| 5. C3×#817 | C2 | semidirect |
| 7. #5189 | C3 | direct (N × H) |
| 18. C2×C3×Q16 | D3 | semidirect |
| 19. C2×C3×Q16 | C2×C3 | semidirect |
| 26. #835 | C2×C3 | semidirect |
| 27. #817 | C2×C3 | semidirect |
| 69. C2×Q16 | C3×D3 | semidirect |
| 133. C32 | #470 | semidirect |
| 162. C3 | #5189 | direct (N × H) |
| 163. C3 | C3×#470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q16 | 2 |
| C3×#946 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C3×#835 | 2 |
| C3×#817 | 2 |
| C3×#470 | 3 |
| #5189 | 3 |