Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#67275 | C2 | semidirect |
| 2. C22×#67273 | C2 | semidirect |
| 3. C22×#67274 | C2 | semidirect |
| 5. C2×#10625046 | C2 | semidirect |
| 6. #13092799 | C2 | direct (N × H) |
| 7. C2×C4×C23⋊C8 | C2 | semidirect |
| 8. C2×C23×#124 | C2 | semidirect |
| 14. C23×#124 | C22 | semidirect |
| 18. C2×#67275 | C22 | semidirect |
| 20. C2×#67274 | C22 | semidirect |
| 22. C2×#67273 | C22 | semidirect |
| 29. #10625046 | C22 | semidirect |
| 30. C4×C23⋊C8 | C22 | semidirect |
| 117. C2×#124 | D23 | semidirect |
| 121. C2×C23 | #495 | semidirect |
| 142. #124 | C2×D23 | semidirect |
| 147. C23 | C2×#495 | semidirect |
| 230. C2 | #13092799 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67275 | 2 |
| C22×#67273 | 2 |
| C22×#67274 | 2 |
| C22×#67272 | 2 |
| C2×#10625046 | 2 |
| #13092799 | 2 |
| C2×C4×C23⋊C8 | 2 |
| C2×C23×#124 | 2 |
| C2×#495 | 23 |