Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
407 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 407 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10592571 | C2 | semidirect |
| 2. #10590869 | C2 | semidirect |
| 3. C2×#63549 | C2 | semidirect |
| 5. C3×#4492 | C2 | semidirect |
| 6. C3×#4491 | C2 | semidirect |
| 7. #10589133 | C2 | semidirect |
| 36. #4492 | D3 | semidirect |
| 37. #4491 | D3 | semidirect |
| 294. C32 | #2210 | semidirect |
| 340. C3 | #69203 | semidirect |
| 341. C3 | #69235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592571 | 2 |
| #10590869 | 2 |
| C2×#63549 | 2 |
| C2×#63546 | 2 |
| C3×#4492 | 2 |
| C3×#4491 | 2 |
| #10589133 | 2 |
| #69235 | 3 |
| #69203 | 3 |