Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
519 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 519 conjugacy classes of subgroups — too many to draw. Only its 106 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. #10592775 | C2 | semidirect |
| 3. C3×#5070 | C2 | semidirect |
| 4. #10590375 | C2 | semidirect |
| 5. #10590311 | C2 | semidirect |
| 6. #10590273 | C2 | semidirect |
| 7. C3⋊C82 | C2 | semidirect |
| 33. #5070 | D3 | semidirect |
| 103. C3⋊(C3⋊C8) | D8 | semidirect |
| 105. C3×C3⋊C8 | SD16 | semidirect |
| 230. C3⋊C8 | #214 | semidirect |
| 287. C32 | #1706 | semidirect |
| 333. C3 | #71180 | semidirect |
| 334. C3 | #71274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592775 | 2 |
| C3×#5073 | 2 |
| C3×#5070 | 2 |
| #10590375 | 2 |
| #10590311 | 2 |
| #10590273 | 2 |
| C3⋊C82 | 2 |
| #71274 | 3 |
| #71180 | 3 |