Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 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×#67273 | C2 | semidirect |
| 3. C2×#10625046 | C2 | semidirect |
| 4. #13092632 | C2 | direct (N × H) |
| 5. C2×C4⋊(C23⋊C8) | C2 | semidirect |
| 6. C2×#10624992 | C2 | semidirect |
| 7. C2×#10624991 | C2 | semidirect |
| 8. C2×C4×D4×C23 | C2 | semidirect |
| 14. C4×D4×C23 | C22 | semidirect |
| 19. C2×#67273 | C22 | semidirect |
| 27. #10625046 | C22 | semidirect |
| 28. #10624992 | C22 | semidirect |
| 29. #10624991 | C22 | semidirect |
| 30. C4⋊(C23⋊C8) | C22 | semidirect |
| 121. C2×C4×D4 | D23 | semidirect |
| 127. C2×C23 | #463 | semidirect |
| 145. C4×D4 | C2×D23 | semidirect |
| 154. C23 | C2×#463 | semidirect |
| 243. C2 | #13092632 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67273 | 2 |
| C22×#67272 | 2 |
| C2×#10625046 | 2 |
| #13092632 | 2 |
| C2×C4⋊(C23⋊C8) | 2 |
| C2×#10624992 | 2 |
| C2×#10624991 | 2 |
| C2×C4×D4×C23 | 2 |
| C2×#463 | 23 |