Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 92 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. #10590763 | C2 | semidirect |
| 3. C3×#4505 | C2 | semidirect |
| 4. C3×#4502 | C2 | semidirect |
| 5. #10589116 | C2 | semidirect |
| 11. #63626 | C4 | semidirect |
| 24. #4505 | D3 | semidirect |
| 25. #4502 | D3 | semidirect |
| 31. #3745 | C2×C4 | semidirect |
| 36. C32×C16 | C2×C4 | semidirect |
| 97. C3×C16 | C4×D3 | semidirect |
| 98. C3×C16 | C4×D3 | semidirect |
| 155. C16 | #624 | semidirect |
| 178. C32 | #2177 | semidirect |
| 207. C3 | #69078 | semidirect |
| 208. C3 | #69339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63626 | 2 |
| #10590763 | 2 |
| C3×#4505 | 2 |
| C3×#4502 | 2 |
| #10589116 | 2 |
| #69339 | 3 |
| #69078 | 3 |