Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
459 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 459 conjugacy classes of subgroups — too many to draw. Only its 104 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. #10592824 | C2 | semidirect |
| 5. C3×#4556 | C2 | semidirect |
| 6. #10589169 | C2 | semidirect |
| 7. #10589157 | C2 | semidirect |
| 32. #4556 | D3 | semidirect |
| 323. C32 | #2081 | semidirect |
| 374. C3 | #69020 | semidirect |
| 375. C3 | #70321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592824 | 2 |
| C3×#5131 | 2 |
| #10591085 | 2 |
| C2×#63558 | 2 |
| C3×#4556 | 2 |
| #10589169 | 2 |
| #10589157 | 2 |
| #70321 | 3 |
| #69020 | 3 |