Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
525 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 525 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 |
|---|---|---|
| 2. C3×#5124 | C2 | semidirect |
| 3. #10591143 | C2 | semidirect |
| 4. #10591141 | C2 | semidirect |
| 7. C3×C3⋊#338 | C2 | semidirect |
| 35. #5124 | D3 | semidirect |
| 37. C3⋊#338 | D3 | semidirect |
| 340. C32 | #2069 | semidirect |
| 390. C3 | #68722 | semidirect |
| 391. C3 | #70730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63650 | 2 |
| C3×#5124 | 2 |
| #10591143 | 2 |
| #10591141 | 2 |
| C2×#63559 | 2 |
| C3×C3⋊#338 | 2 |
| #70730 | 3 |
| #68722 | 3 |