Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
315 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 315 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 |
|---|---|---|
| 2. #10590621 | C2 | semidirect |
| 3. #10589329 | C2 | semidirect |
| 4. C3×C4×C3⋊C16 | C2 | semidirect |
| 5. #10589112 | C2 | semidirect |
| 28. C4×C3⋊C16 | D3 | semidirect |
| 191. C32 | #2170 | semidirect |
| 218. C3 | #69056 | semidirect |
| 219. C3 | #70923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4700 | 2 |
| #10590621 | 2 |
| #10589329 | 2 |
| C3×C4×C3⋊C16 | 2 |
| #10589112 | 2 |
| #70923 | 3 |
| #69056 | 3 |