Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
347 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 347 conjugacy classes of subgroups — too many to draw. Only its 86 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×#4850 | C2 | semidirect |
| 4. #10590250 | C2 | semidirect |
| 5. #10589346 | C2 | semidirect |
| 7. #10589095 | C2 | semidirect |
| 31. #4850 | D3 | semidirect |
| 282. C32 | #1678 | semidirect |
| 327. C3 | #68410 | semidirect |
| 328. C3 | #71150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4850 | 2 |
| #10590364 | 2 |
| #10590277 | 2 |
| #10590250 | 2 |
| #10589346 | 2 |
| C3×#4485 | 2 |
| #10589095 | 2 |
| #71150 | 3 |
| #68410 | 3 |