Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
510 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 107 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. #10592890 | C2 | semidirect |
| 2. C2×#63655 | C2 | semidirect |
| 4. #10592571 | C2 | semidirect |
| 5. C32×#358 | C2 | semidirect |
| 6. #10589367 | C2 | semidirect |
| 7. #10589357 | C2 | semidirect |
| 26. C3×#358 | D3 | semidirect |
| 85. #358 | C3⋊D3 | semidirect |
| 188. C32 | #2210 | semidirect |
| 224. C3 | #69235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592890 | 2 |
| C2×#63655 | 2 |
| C2×#63626 | 2 |
| #10592571 | 2 |
| C32×#358 | 2 |
| #10589367 | 2 |
| #10589357 | 2 |
| #69235 | 3 |