Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 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 |
|---|---|---|
| 2. C22×#67274 | C2 | semidirect |
| 3. C2×#10625117 | C2 | semidirect |
| 4. #13092578 | C2 | direct (N × H) |
| 5. C2×#10625017 | C2 | semidirect |
| 6. C2×#10625003 | C2 | semidirect |
| 7. C2×(C2×D23)⋊C8 | C2 | semidirect |
| 8. C22×Q16×C23 | C2 | semidirect |
| 20. C2×Q16×C23 | C22 | semidirect |
| 23. #10625117 | C22 | semidirect |
| 25. C2×#67274 | C22 | semidirect |
| 30. #10625017 | C22 | semidirect |
| 31. #10625003 | C22 | semidirect |
| 32. (C2×D23)⋊C8 | C22 | semidirect |
| 131. C22×Q16 | D23 | semidirect |
| 138. C2×C23 | #452 | semidirect |
| 155. C2×Q16 | C2×D23 | semidirect |
| 168. C23 | C2×#452 | semidirect |
| 267. C2 | #13092578 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67292 | 2 |
| C22×#67274 | 2 |
| C2×#10625117 | 2 |
| #13092578 | 2 |
| C2×#10625017 | 2 |
| C2×#10625003 | 2 |
| C2×(C2×D23)⋊C8 | 2 |
| C22×Q16×C23 | 2 |
| C2×#452 | 23 |