Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
431 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 114 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×#5079 | C2 | semidirect |
| 3. C3×#5078 | C2 | semidirect |
| 6. C3×#4681 | C2 | semidirect |
| 7. C3×#4455 | C2 | semidirect |
| 9. #71189 | C3 | direct (N × H) |
| 31. #5079 | C2×C3 | semidirect |
| 32. #5078 | C2×C3 | semidirect |
| 35. #4681 | C2×C3 | semidirect |
| 37. #4455 | C2×C3 | semidirect |
| 265. C32 | #1719 | semidirect |
| 305. C3 | #71189 | direct (N × H) |
| 306. C3 | C3×#1719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#486 | 2 |
| C3×#5079 | 2 |
| C3×#5078 | 2 |
| C3×#5076 | 2 |
| C3×#5070 | 2 |
| C3×#4681 | 2 |
| C3×#4455 | 2 |
| C3×#1719 | 3 |
| #71189 | 3 |