Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
297 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 112 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. C3⋊(C3⋊C16) | Q8 | semidirect |
| 54. #627 | C16 | semidirect |
| 146. C32 | Q8×C16 | semidirect |
| 171. C3 | #69280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#627 | 2 |
| C16×C3⋊Dic3 | 2 |
| C3×Dic3⋊C16 | 2 |
| #10589133 | 2 |
| Dic3×C3⋊C16 | 2 |
| #69280 | 3 |