Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
350 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 350 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 |
|---|---|---|
| 1. #10592841 | C2 | semidirect |
| 2. C3×#5142 | C2 | semidirect |
| 3. C3×#5140 | C2 | semidirect |
| 4. C2×#63546 | C2 | semidirect |
| 5. #10589143 | C2 | semidirect |
| 6. #10589128 | C2 | semidirect |
| 7. #10589127 | C2 | semidirect |
| 31. #5142 | D3 | semidirect |
| 32. #5140 | D3 | semidirect |
| 288. C32 | #2221 | semidirect |
| 329. C3 | #71092 | semidirect |
| 330. C3 | #71454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592841 | 2 |
| C3×#5142 | 2 |
| C3×#5140 | 2 |
| C2×#63546 | 2 |
| #10589143 | 2 |
| #10589128 | 2 |
| #10589127 | 2 |
| #71454 | 3 |
| #71092 | 3 |