Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
743 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 743 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 1. C3×#5748 | C2 | semidirect |
| 2. #10594786 | C2 | semidirect |
| 3. C3×#5129 | C2 | semidirect |
| 4. #10591070 | C2 | semidirect |
| 5. #10589426 | C2 | semidirect |
| 26. #5748 | D3 | semidirect |
| 29. #5129 | D3 | semidirect |
| 338. C32 | #2017 | semidirect |
| 390. C3 | #70013 | semidirect |
| 391. C3 | #72121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5748 | 2 |
| #10594786 | 2 |
| C3×#5129 | 2 |
| #10591070 | 2 |
| #10589426 | 2 |
| #72121 | 3 |
| #70013 | 3 |