Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
534 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 120 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. #10590248 | C2 | semidirect |
| 3. #10589410 | C2 | semidirect |
| 4. C3×#4544 | C2 | semidirect |
| 5. #10589095 | C2 | semidirect |
| 28. #4544 | D3 | semidirect |
| 239. C32 | #1543 | semidirect |
| 281. C3 | #68382 | semidirect |
| 282. C3 | #71805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5716 | 2 |
| #10590248 | 2 |
| #10589410 | 2 |
| C3×#4544 | 2 |
| #10589095 | 2 |
| #71805 | 3 |
| #68382 | 3 |