Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
390 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 32. #3746 | Q8 | semidirect |
| 127. C32 | #2225 | semidirect |
| 151. C3 | #71389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#500 | 2 |
| C4×#3746 | 2 |
| #10589358 | 2 |
| #10589356 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #71389 | 3 |