Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
359 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 359 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 3. C3×#4682 | C2 | semidirect |
| 4. C32×#334 | C2 | semidirect |
| 5. C3×#4482 | C2 | semidirect |
| 7. #68542 | C3 | direct (N × H) |
| 24. #4682 | C2×C3 | semidirect |
| 26. C3×#334 | D3 | semidirect |
| 27. C3×#334 | C2×C3 | semidirect |
| 29. #4482 | C2×C3 | semidirect |
| 82. C32×C8 | SD16 | semidirect |
| 87. #334 | C3×D3 | semidirect |
| 175. C3×C8 | #204 | semidirect |
| 176. C3×C8 | C3×SD16 | semidirect |
| 221. C32 | #1693 | semidirect |
| 236. C8 | C3×#204 | semidirect |
| 259. C3 | #68542 | direct (N × H) |
| 260. C3 | C3×#1693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4841 | 2 |
| C3×#4688 | 2 |
| C3×#4682 | 2 |
| C32×#334 | 2 |
| C3×#4482 | 2 |
| C3×#1693 | 3 |
| #68542 | 3 |