Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
305 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 305 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×#4680 | C2 | semidirect |
| 4. C3×#4494 | C2 | semidirect |
| 5. C3×#4463 | C2 | semidirect |
| 7. #70919 | C3 | direct (N × H) |
| 21. #4680 | C2×C3 | semidirect |
| 26. #4494 | C2×C3 | semidirect |
| 27. #4463 | C2×C3 | semidirect |
| 30. C32×Q16 | Q8 | semidirect |
| 32. C32×D8 | Q8 | semidirect |
| 90. C3×Q16 | Dic6 | semidirect |
| 91. C3×Q16 | C3×Q8 | semidirect |
| 96. C3×D8 | Dic6 | semidirect |
| 97. C3×D8 | C3×Q8 | semidirect |
| 180. Q16 | C3×Dic6 | semidirect |
| 182. D8 | C3×Dic6 | semidirect |
| 212. C32 | #2230 | semidirect |
| 243. C3 | #70919 | direct (N × H) |
| 244. C3 | C3×#2230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#443 | 2 |
| C3×#4680 | 2 |
| C3×#4566 | 2 |
| C3×#4494 | 2 |
| C3×#4463 | 2 |
| C3×#2230 | 3 |
| #70919 | 3 |