Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
171 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 171 conjugacy classes of subgroups — too many to draw. Only its 62 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. C32×#367 | C2 | semidirect |
| 3. C3×#4499 | C2 | semidirect |
| 5. #67580 | C3 | direct (N × H) |
| 9. C3×Dic24 | C4 | semidirect |
| 11. C3×D48 | C4 | semidirect |
| 17. C3×#367 | D3 | semidirect |
| 18. C3×#367 | C2×C3 | semidirect |
| 19. #4499 | C2×C3 | semidirect |
| 40. Dic24 | C3×C4 | semidirect |
| 42. D48 | C3×C4 | semidirect |
| 55. #367 | C3×D3 | semidirect |
| 136. C32 | #1418 | semidirect |
| 160. C3 | #67580 | direct (N × H) |
| 161. C3 | C3×#1418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4904 | 2 |
| C32×#367 | 2 |
| C3×#4499 | 2 |
| C3×#1418 | 3 |
| #67580 | 3 |