Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
499 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 499 conjugacy classes of subgroups — too many to draw. Only its 102 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. #10592769 | C2 | semidirect |
| 3. C3×#5070 | C2 | semidirect |
| 4. #10590375 | C2 | semidirect |
| 5. #10590369 | C2 | semidirect |
| 6. #10590303 | C2 | semidirect |
| 7. #10589078 | C2 | semidirect |
| 33. #5070 | D3 | semidirect |
| 105. C3×C3⋊C8 | SD16 | semidirect |
| 229. C3⋊C8 | #214 | semidirect |
| 286. C32 | #1715 | semidirect |
| 332. C3 | #71185 | semidirect |
| 333. C3 | #71277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592769 | 2 |
| C3×#5073 | 2 |
| C3×#5070 | 2 |
| #10590375 | 2 |
| #10590369 | 2 |
| #10590303 | 2 |
| #10589078 | 2 |
| #71277 | 3 |
| #71185 | 3 |