Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
309 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 309 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 |
| 3. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 4. #10589140 | C2 | semidirect |
| 20. #4682 | D3 | semidirect |
| 39. C3×D24 | Q8 | semidirect |
| 106. D24 | Dic6 | semidirect |
| 203. C32 | #2224 | semidirect |
| 239. C3 | #70886 | semidirect |
| 240. C3 | #71387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D24 | 2 |
| C3×#4682 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #10589140 | 2 |
| #10589114 | 2 |
| #71387 | 3 |
| #70886 | 3 |