Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
354 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 2. C32×C4⋊C16 | C2 | semidirect |
| 3. #10589324 | C2 | semidirect |
| 12. C3×C4⋊C16 | D3 | semidirect |
| 46. C4⋊C16 | C3⋊D3 | semidirect |
| 111. C32 | #1361 | semidirect |
| 138. C3 | #67560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592394 | 2 |
| C32×C4⋊C16 | 2 |
| #10589324 | 2 |
| #67560 | 3 |