Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
289 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 289 conjugacy classes of subgroups — too many to draw. Only its 68 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. #10590912 | C2 | semidirect |
| 3. #10589353 | C2 | semidirect |
| 4. C3×#4487 | C2 | semidirect |
| 5. #10589127 | C2 | semidirect |
| 6. #10589126 | C2 | semidirect |
| 7. #10589109 | C2 | semidirect |
| 35. #4487 | D3 | semidirect |
| 240. C32 | #2238 | semidirect |
| 277. C3 | #69313 | semidirect |
| 278. C3 | #71088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4865 | 2 |
| #10590912 | 2 |
| #10589353 | 2 |
| C3×#4487 | 2 |
| #10589127 | 2 |
| #10589126 | 2 |
| #10589109 | 2 |
| #71088 | 3 |
| #69313 | 3 |