Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
501 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 501 conjugacy classes of subgroups — too many to draw. Only its 98 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. #10591141 | C2 | semidirect |
| 5. C3×#4559 | C2 | semidirect |
| 6. C3×#4556 | C2 | semidirect |
| 7. #10589157 | C2 | semidirect |
| 32. #4559 | D3 | semidirect |
| 33. #4556 | D3 | semidirect |
| 338. C32 | #2081 | semidirect |
| 390. C3 | #69020 | semidirect |
| 391. C3 | #69021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63650 | 2 |
| #10591141 | 2 |
| #10591096 | 2 |
| C3×#4559 | 2 |
| C3×#4556 | 2 |
| #10589157 | 2 |
| #69021 | 3 |
| #69020 | 3 |