Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
403 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 403 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. C3×#4679 | C2 | semidirect |
| 4. C3×#4454 | C2 | semidirect |
| 5. #10589099 | C2 | semidirect |
| 6. #10589084 | C2 | semidirect |
| 31. #4679 | D3 | semidirect |
| 39. #4454 | D3 | semidirect |
| 301. C32 | #1585 | semidirect |
| 347. C3 | #68080 | semidirect |
| 348. C3 | #70954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C4⋊(C3⋊D3) | 2 |
| C3×#4679 | 2 |
| C4×#3717 | 2 |
| C3×#4454 | 2 |
| #10589099 | 2 |
| #10589084 | 2 |
| #10589082 | 2 |
| #70954 | 3 |
| #68080 | 3 |