Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
171 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 171 conjugacy classes of subgroups — too many to draw. Only its 58 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. #10589371 | C2 | semidirect |
| 3. C3×#4499 | C2 | semidirect |
| 9. C3×Dic24 | C4 | semidirect |
| 11. C3×D48 | C4 | semidirect |
| 19. #4499 | D3 | semidirect |
| 40. Dic24 | Dic3 | semidirect |
| 42. D48 | Dic3 | semidirect |
| 136. C32 | #1418 | semidirect |
| 160. C3 | #67606 | semidirect |
| 161. C3 | #67828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4904 | 2 |
| #10589371 | 2 |
| C3×#4499 | 2 |
| #67828 | 3 |
| #67606 | 3 |