Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
341 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 108 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. C3×#4461 | C2 | semidirect |
| 3. C3×C4×C3⋊C16 | C2 | semidirect |
| 4. #10589133 | C2 | semidirect |
| 26. #4461 | D3 | semidirect |
| 27. C4×C3⋊C16 | D3 | semidirect |
| 210. C32 | #2164 | semidirect |
| 240. C3 | #69053 | semidirect |
| 241. C3 | #69074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592388 | 2 |
| C3×#4461 | 2 |
| C3×C4×C3⋊C16 | 2 |
| #10589133 | 2 |
| #10589108 | 2 |
| #69074 | 3 |
| #69053 | 3 |