Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
830 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 92 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. #10590379 | C2 | semidirect |
| 4. #10590313 | C2 | semidirect |
| 5. C3×#4544 | C2 | semidirect |
| 6. #10589082 | C2 | semidirect |
| 7. #10589082 | C2 | semidirect |
| 18. C3×#869 | C22 | semidirect |
| 21. C3×C4⋊(C3⋊C8) | C22 | semidirect |
| 22. C3×C4⋊(C3⋊C8) | C22 | semidirect |
| 23. C3×C4×C3⋊C8 | C22 | semidirect |
| 33. #5070 | D3 | semidirect |
| 37. #4544 | D3 | semidirect |
| 97. #869 | C2×D3 | semidirect |
| 109. C4⋊(C3⋊C8) | C2×D3 | semidirect |
| 110. C4⋊(C3⋊C8) | C2×D3 | semidirect |
| 111. C4×C3⋊C8 | C2×D3 | semidirect |
| 133. C4⋊(C3⋊D3) | SD16 | semidirect |
| 440. C32 | #1639 | semidirect |
| 511. C3 | #68392 | semidirect |
| 512. C3 | #71198 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596188 | 2 |
| C3×#5070 | 2 |
| #10590379 | 2 |
| #10590313 | 2 |
| C3×#4544 | 2 |
| #10589082 | 2 |
| #71198 | 3 |
| #68392 | 3 |