Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
309 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. #10589358 | C2 | semidirect |
| 4. C3×#4490 | C2 | semidirect |
| 5. #10589142 | C2 | semidirect |
| 6. #10589119 | C2 | semidirect |
| 35. #4490 | D3 | semidirect |
| 248. C32 | #2235 | semidirect |
| 287. C3 | #69352 | semidirect |
| 288. C3 | #70602 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D3×#107 | 2 |
| #10590852 | 2 |
| #10589358 | 2 |
| C3×#4490 | 2 |
| #10589142 | 2 |
| #10589119 | 2 |
| (C2×D3)⋊(C3⋊C16) | 2 |
| #70602 | 3 |
| #69352 | 3 |