Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
658 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5070 | C2 | semidirect |
| 3. #10590363 | C2 | semidirect |
| 4. #10590269 | C2 | semidirect |
| 5. #10589410 | C2 | semidirect |
| 6. #10589081 | C2 | semidirect |
| 7. #10589081 | C2 | semidirect |
| 18. C3×#869 | C22 | semidirect |
| 20. C4⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 21. C4⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 23. C3×C4×C3⋊C8 | C22 | semidirect |
| 32. #5070 | D3 | semidirect |
| 90. #869 | C2×D3 | semidirect |
| 106. C4×C3⋊C8 | C2×D3 | semidirect |
| 129. C3×D12 | SD16 | semidirect |
| 302. D12 | #214 | semidirect |
| 397. C32 | #1639 | semidirect |
| 466. C3 | #71198 | semidirect |
| 467. C3 | #71908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5717 | 2 |
| C3×#5070 | 2 |
| #10590363 | 2 |
| #10590269 | 2 |
| #10589410 | 2 |
| #10589081 | 2 |
| #71908 | 3 |
| #71198 | 3 |