Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
455 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 455 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 2. #10591141 | C2 | semidirect |
| 5. #10589397 | C2 | semidirect |
| 6. C3×#4533 | C2 | semidirect |
| 7. #10589171 | C2 | semidirect |
| 32. #4533 | D3 | semidirect |
| 324. C32 | #2081 | semidirect |
| 375. C3 | #69020 | semidirect |
| 376. C3 | #70322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5001 | 2 |
| #10591141 | 2 |
| #10591086 | 2 |
| C2×#63558 | 2 |
| #10589397 | 2 |
| C3×#4533 | 2 |
| #10589171 | 2 |
| #70322 | 3 |
| #69020 | 3 |