Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
405 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 405 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10592854 | C2 | semidirect |
| 3. #10590777 | C2 | semidirect |
| 4. C2×#63548 | C2 | semidirect |
| 5. C3×#4562 | C2 | semidirect |
| 6. #10589133 | C2 | semidirect |
| 7. #10589119 | C2 | semidirect |
| 33. #4562 | D3 | semidirect |
| 298. C32 | #2210 | semidirect |
| 344. C3 | #69203 | semidirect |
| 345. C3 | #71463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592854 | 2 |
| C2×C3×#826 | 2 |
| #10590777 | 2 |
| C2×#63548 | 2 |
| C3×#4562 | 2 |
| #10589133 | 2 |
| #10589119 | 2 |
| #71463 | 3 |
| #69203 | 3 |