Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#10625095 | C2 | semidirect |
| 4. #13092579 | C2 | direct (N × H) |
| 5. C2×#10625017 | C2 | semidirect |
| 6. C2×#10625014 | C2 | semidirect |
| 7. C2×C22⋊(C23⋊C8) | C2 | semidirect |
| 21. C2×#67275 | C22 | semidirect |
| 23. C2×#67273 | C22 | semidirect |
| 26. #10625095 | C22 | semidirect |
| 30. #10625017 | C22 | semidirect |
| 31. #10625014 | C22 | semidirect |
| 32. C22⋊(C23⋊C8) | C22 | semidirect |
| 140. C2×C23 | #452 | semidirect |
| 168. C23 | C2×#452 | semidirect |
| 267. C2 | #13092579 | 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 |
| C2×#10625095 | 2 |
| #13092579 | 2 |
| C2×#10625017 | 2 |
| C2×#10625014 | 2 |
| C2×C22⋊(C23⋊C8) | 2 |
| C22×#41×C23 | 2 |
| C2×#452 | 23 |