Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
407 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 407 conjugacy classes of subgroups — too many to draw. Only its 96 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. #10590301 | C2 | semidirect |
| 5. C3×#4458 | C2 | semidirect |
| 6. #10589094 | C2 | semidirect |
| 33. #4679 | D3 | semidirect |
| 39. #4458 | D3 | semidirect |
| 112. C32×C8 | SD16 | semidirect |
| 250. C3×C8 | #204 | semidirect |
| 251. C3×C8 | #215 | semidirect |
| 312. C32 | #1686 | semidirect |
| 333. C8 | #3717 | semidirect |
| 359. C3 | #68592 | semidirect |
| 360. C3 | #70958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592392 | 2 |
| C3×#4679 | 2 |
| #10590367 | 2 |
| #10590301 | 2 |
| C3×#4458 | 2 |
| #10589094 | 2 |
| #10589091 | 2 |
| #70958 | 3 |
| #68592 | 3 |