Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1949 conjugacy classes of subgroups; only the 322 normal subgroups are shown.
This group has 1949 conjugacy classes of subgroups — too many to draw. Only its 322 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 |
|---|---|---|
| 1. C32×#585 | C2 | semidirect |
| 2. C3×#5830 | C2 | semidirect |
| 3. C3×#5244 | C2 | semidirect |
| 4. C3×#5240 | C2 | semidirect |
| 6. #84126 | C3 | direct (N × H) |
| 12. C22×C3×D12 | C22 | semidirect |
| 15. C3×#937 | C22 | semidirect |
| 17. C3×#926 | C22 | semidirect |
| 18. C3×#834 | C22 | semidirect |
| 20. C3×#585 | D3 | semidirect |
| 21. C3×#585 | C2×C3 | semidirect |
| 23. #5830 | C2×C3 | semidirect |
| 26. #5244 | C2×C3 | semidirect |
| 27. #5240 | C2×C3 | semidirect |
| 35. C2×C32×Q8 | D4 | semidirect |
| 38. C2×C32×D4 | D4 | semidirect |
| 41. C22×C32×C4 | D4 | semidirect |
| 67. C22×D12 | C22×C3 | semidirect |
| 75. #937 | C22×C3 | semidirect |
| 77. #926 | C22×C3 | semidirect |
| 79. #834 | C22×C3 | semidirect |
| 100. #585 | C3×D3 | semidirect |
| 125. C2×C3×Q8 | #67 | semidirect |
| 126. C2×C3×Q8 | C3×D4 | semidirect |
| 138. C2×C3×D4 | #67 | semidirect |
| 139. C2×C3×D4 | C3×D4 | semidirect |
| 147. C22×C3×C4 | #67 | semidirect |
| 148. C22×C3×C4 | C3×D4 | semidirect |
| 250. C2×Q8 | C3×#67 | semidirect |
| 256. C2×D4 | C3×#67 | semidirect |
| 259. C22×C4 | C3×#67 | semidirect |
| 295. C32 | #3027 | semidirect |
| 339. C3 | #84126 | direct (N × H) |
| 340. C3 | C3×#3027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#585 | 2 |
| C3×#5830 | 2 |
| C3×#5244 | 2 |
| C3×#5240 | 2 |
| C3×#3027 | 3 |
| #84126 | 3 |