Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
327 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 72 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. C3×#5160 | C2 | semidirect |
| 2. C2×C3×#826 | C2 | semidirect |
| 3. #10590926 | C2 | semidirect |
| 4. #10590621 | C2 | semidirect |
| 5. #10589429 | C2 | semidirect |
| 6. #10589143 | C2 | semidirect |
| 7. #10589126 | C2 | semidirect |
| 28. #5160 | D3 | semidirect |
| 29. C2×#826 | D3 | semidirect |
| 274. C32 | #2221 | semidirect |
| 314. C3 | #71092 | semidirect |
| 315. C3 | #71472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5160 | 2 |
| C2×C3×#826 | 2 |
| #10590926 | 2 |
| #10590621 | 2 |
| #10589429 | 2 |
| #10589143 | 2 |
| #10589126 | 2 |
| #71472 | 3 |
| #71092 | 3 |