Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
480 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 241 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 |
|---|---|---|
| 22. C32×M16 | C8 | semidirect |
| 64. C3×M16 | C3⋊C8 | semidirect |
| 119. M16 | C3⋊(C3⋊C8) | semidirect |
| 140. C32 | #1283 | semidirect |
| 173. C3 | #67668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×M16 | 2 |
| #10592624 | 2 |
| C2×C4⋊(C3⋊(C3⋊C8)) | 2 |
| #67668 | 3 |