Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
315 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 315 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×#4700 | C2 | semidirect |
| 3. C32×#346 | C2 | semidirect |
| 4. C3×#4510 | C2 | semidirect |
| 5. C3×#4506 | C2 | semidirect |
| 7. #69085 | C3 | direct (N × H) |
| 15. C3×Dic24 | C4 | semidirect |
| 16. C3×#800 | C4 | semidirect |
| 17. C3×D48 | C4 | semidirect |
| 21. #4700 | C2×C3 | semidirect |
| 25. C3×#346 | D3 | semidirect |
| 26. C3×#346 | C2×C3 | semidirect |
| 27. #4510 | C2×C3 | semidirect |
| 28. #4506 | C2×C3 | semidirect |
| 63. Dic24 | C3×C4 | semidirect |
| 64. #800 | C3×C4 | semidirect |
| 65. D48 | C3×C4 | semidirect |
| 80. #346 | C3×D3 | semidirect |
| 186. C32 | #2179 | semidirect |
| 212. C3 | #69085 | direct (N × H) |
| 213. C3 | C3×#2179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4904 | 2 |
| C3×#4700 | 2 |
| C32×#346 | 2 |
| C3×#4510 | 2 |
| C3×#4506 | 2 |
| C3×#2179 | 3 |
| #69085 | 3 |