Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10625075 | C2 | semidirect |
| 2. #13092847 | C2 | direct (N × H) |
| 3. C2×#10625011 | C2 | semidirect |
| 4. C2×#10625009 | C2 | semidirect |
| 5. C2×#10625010 | C2 | semidirect |
| 6. C2×#10625008 | C2 | semidirect |
| 7. C22×C23⋊C16 | C2 | semidirect |
| 8. C2×C23×#135 | C2 | semidirect |
| 12. C23×#135 | C22 | semidirect |
| 19. #10625075 | C22 | semidirect |
| 22. #10625011 | C22 | semidirect |
| 23. #10625010 | C22 | semidirect |
| 24. #10625009 | C22 | semidirect |
| 25. #10625008 | C22 | semidirect |
| 28. C2×C23⋊C16 | C22 | semidirect |
| 96. C2×#135 | D23 | semidirect |
| 105. C2×C23 | #508 | semidirect |
| 113. #135 | C2×D23 | semidirect |
| 128. C23 | C2×#508 | semidirect |
| 197. C2 | #13092847 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625075 | 2 |
| #13092847 | 2 |
| C2×#10625011 | 2 |
| C2×#10625009 | 2 |
| C2×#10625010 | 2 |
| C2×#10625008 | 2 |
| C22×C23⋊C16 | 2 |
| C2×C23×#135 | 2 |
| C2×#508 | 23 |