Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
506 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 149 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. #10709931 | C2 | semidirect |
| 2. #10709929 | C2 | semidirect |
| 4. C16×C3⋊C16 | C2 | semidirect |
| 88. C3×C16 | SD32 | semidirect |
| 89. C3⋊C16 | SD32 | semidirect |
| 132. C16 | #827 | semidirect |
| 161. C3 | #123411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10709931 | 2 |
| #10709929 | 2 |
| #10709904 | 2 |
| C16×C3⋊C16 | 2 |
| C3×#12517 | 2 |
| #123411 | 3 |