Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
305 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 305 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4680 | C2 | semidirect |
| 3. C3×#4463 | C2 | semidirect |
| 4. #10589136 | C2 | semidirect |
| 21. #4680 | D3 | semidirect |
| 27. #4463 | D3 | semidirect |
| 34. #3746 | Q8 | semidirect |
| 35. #3745 | Q8 | semidirect |
| 212. C32 | #2230 | semidirect |
| 243. C3 | #69307 | semidirect |
| 244. C3 | #71350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592399 | 2 |
| C3×#4680 | 2 |
| C3×#4463 | 2 |
| #10589136 | 2 |
| #10589125 | 2 |
| #71350 | 3 |
| #69307 | 3 |