Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
402 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 29. C32×C16 | Q8 | semidirect |
| 45. #634 | C16 | direct (N × H) |
| 64. C3×C16 | Dic6 | semidirect |
| 104. C16 | #634 | direct (N × H) |
| 112. C32 | Q8×C16 | semidirect |
| 133. C3 | C16×Dic6 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#634 | 2 |
| C32×C4×C16 | 2 |
| #10589367 | 2 |
| C16×C3⋊Dic3 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| C16×Dic6 | 3 |