Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
450 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 107 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⋊D3×#107 | C2 | semidirect |
| 3. C32×#367 | C2 | semidirect |
| 4. #10589375 | C2 | semidirect |
| 5. #10589373 | C2 | semidirect |
| 6. #10589357 | C2 | semidirect |
| 7. #10589356 | C2 | semidirect |
| 22. C3×#367 | D3 | semidirect |
| 75. #367 | C3⋊D3 | semidirect |
| 171. C32 | #2233 | semidirect |
| 206. C3 | #69350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592582 | 2 |
| C3⋊D3×#107 | 2 |
| C32×#367 | 2 |
| #10589375 | 2 |
| #10589373 | 2 |
| #10589357 | 2 |
| #10589356 | 2 |
| #69350 | 3 |