Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
378 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 30. C3⋊(C3⋊C16) | Q8 | semidirect |
| 112. C32 | #2183 | semidirect |
| 133. C3 | #70949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C8×Q8 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #10589327 | 2 |
| C4×C3⋊(C3⋊C16) | 2 |
| #70949 | 3 |