Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
317 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 317 conjugacy classes of subgroups — too many to draw. Only its 98 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×#5106 | C2 | semidirect |
| 3. C32×C22⋊C16 | C2 | semidirect |
| 4. C3×#4509 | C2 | semidirect |
| 5. C3×#4509 | C2 | semidirect |
| 6. C3×#4505 | C2 | semidirect |
| 7. C3×#4504 | C2 | semidirect |
| 9. #69097 | C3 | direct (N × H) |
| 24. #5106 | C2×C3 | semidirect |
| 30. C3×C22⋊C16 | D3 | semidirect |
| 31. C3×C22⋊C16 | C2×C3 | semidirect |
| 32. #4509 | C2×C3 | semidirect |
| 33. #4509 | C2×C3 | semidirect |
| 34. #4505 | C2×C3 | semidirect |
| 35. #4504 | C2×C3 | semidirect |
| 100. C22⋊C16 | C3×D3 | semidirect |
| 259. C32 | #2234 | semidirect |
| 303. C3 | #69097 | direct (N × H) |
| 304. C3 | C3×#2234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5115 | 2 |
| C3×#5106 | 2 |
| C32×C22⋊C16 | 2 |
| C3×#4509 | 2 |
| C3×#4505 | 2 |
| C3×#4504 | 2 |
| C3×#2234 | 3 |
| #69097 | 3 |