Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#10625083 | C2 | semidirect |
| 2. C2×D8×D23 | C2 | semidirect |
| 3. #13092851 | C2 | direct (N × H) |
| 4. C2×#10624982 | C2 | semidirect |
| 5. C2×#10625009 | C2 | semidirect |
| 6. C2×#10625008 | C2 | semidirect |
| 7. C2×#10624980 | C2 | semidirect |
| 8. C2×C23×D16 | C2 | semidirect |
| 12. C2×D8×C23 | C22 | semidirect |
| 16. #10625083 | C22 | semidirect |
| 18. D8×D23 | C22 | semidirect |
| 19. C2×Dic92 | C22 | semidirect |
| 22. C23×D16 | C22 | semidirect |
| 23. C2×C16×C23 | C22 | semidirect |
| 24. #10625009 | C22 | semidirect |
| 25. #10625008 | C22 | semidirect |
| 26. C2×C23⋊C16 | C22 | semidirect |
| 27. #10624982 | C22 | semidirect |
| 28. #10624980 | C22 | semidirect |
| 45. D8×C23 | C23 | semidirect |
| 51. Dic92 | C23 | semidirect |
| 56. C16×C23 | C23 | semidirect |
| 57. C23⋊C16 | C23 | semidirect |
| 104. C2×D16 | D23 | semidirect |
| 108. C2×C23 | #509 | semidirect |
| 123. C2×D8 | C2×D23 | semidirect |
| 128. D16 | C2×D23 | semidirect |
| 131. C2×C16 | C2×D23 | semidirect |
| 132. C23 | C2×#509 | semidirect |
| 155. D8 | C22×D23 | semidirect |
| 161. C16 | C22×D23 | semidirect |
| 205. C2 | #13092851 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625083 | 2 |
| C2×D8×D23 | 2 |
| #13092851 | 2 |
| C2×#10624982 | 2 |
| C2×#10625009 | 2 |
| C2×#10625008 | 2 |
| C2×#10624980 | 2 |
| C2×C23×D16 | 2 |
| C2×#509 | 23 |