Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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. #10589415 | C2 | semidirect |
| 33. C23×C32 | C16 | semidirect |
| 83. C23×C3 | C3⋊C16 | semidirect |
| 128. C32 | #1314 | semidirect |
| 133. C23 | C3⋊(C3⋊C16) | semidirect |
| 166. C3 | #67673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C22⋊C8 | 2 |
| #10589415 | 2 |
| #67673 | 3 |