Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
411 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 411 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×#4682 | C2 | semidirect |
| 4. C3×#4458 | C2 | semidirect |
| 5. #10589093 | C2 | semidirect |
| 25. #4682 | D3 | semidirect |
| 29. #4458 | D3 | semidirect |
| 85. C32×C8 | SD16 | semidirect |
| 190. C3×C8 | #204 | semidirect |
| 191. C3×C8 | #215 | semidirect |
| 246. C32 | #1673 | semidirect |
| 262. C8 | #3717 | semidirect |
| 287. C3 | #68578 | semidirect |
| 288. C3 | #71371 | 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×#4682 | 2 |
| #10590379 | 2 |
| C3×#4458 | 2 |
| #10589093 | 2 |
| #71371 | 3 |
| #68578 | 3 |