Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
595 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 595 conjugacy classes of subgroups — too many to draw. Only its 110 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. #10592817 | C2 | semidirect |
| 3. C2×#63568 | C2 | semidirect |
| 4. #10591076 | C2 | semidirect |
| 5. C3×C3⋊#338 | C2 | semidirect |
| 31. C3⋊#338 | D3 | semidirect |
| 300. C32 | #2050 | semidirect |
| 345. C3 | #68719 | semidirect |
| 346. C3 | #72117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5748 | 2 |
| #10592817 | 2 |
| C2×#63568 | 2 |
| #10591076 | 2 |
| C3×C3⋊#338 | 2 |
| #72117 | 3 |
| #68719 | 3 |