Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
837 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 837 conjugacy classes of subgroups — too many to draw. Only its 164 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×#4925 | C2 | semidirect |
| 3. #10589146 | C2 | semidirect |
| 18. #4925 | D3 | semidirect |
| 27. C2×C4⋊(C3⋊D3) | C8 | semidirect |
| 241. C32 | #1460 | semidirect |
| 290. C3 | #70783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊(C3⋊D3) | 2 |
| C3×#4925 | 2 |
| #10589146 | 2 |
| #70783 | 3 |