Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 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×#67263 | C2 | semidirect |
| 2. C22×#67273 | C2 | semidirect |
| 3. C22×#67272 | C2 | semidirect |
| 4. C2×#10625111 | C2 | semidirect |
| 5. C2×#10625107 | C2 | semidirect |
| 6. #13092805 | C2 | direct (N × H) |
| 7. C2×#10624997 | C2 | semidirect |
| 8. C22×D8×C23 | C2 | semidirect |
| 15. C2×D8×C23 | C22 | semidirect |
| 19. #10625111 | C22 | semidirect |
| 21. #10625107 | C22 | semidirect |
| 23. C2×#67273 | C22 | semidirect |
| 25. C2×#67272 | C22 | semidirect |
| 29. C2×#67263 | C22 | semidirect |
| 30. #10624997 | C22 | semidirect |
| 56. C2×C8×C23 | D4 | semidirect |
| 63. C2×C23⋊C8 | D4 | semidirect |
| 97. C8×C23 | C2×D4 | semidirect |
| 98. C23⋊C8 | C2×D4 | semidirect |
| 120. C22×D8 | D23 | semidirect |
| 127. C2×C23 | #496 | semidirect |
| 143. C2×D8 | C2×D23 | semidirect |
| 153. C23 | C2×#496 | semidirect |
| 184. C2×C8 | C22⋊D23 | semidirect |
| 221. C8 | C2×C22⋊D23 | semidirect |
| 242. C2 | #13092805 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67263 | 2 |
| C22×#67273 | 2 |
| C22×#67272 | 2 |
| C2×#10625111 | 2 |
| C2×#10625107 | 2 |
| #13092805 | 2 |
| C2×#10624997 | 2 |
| C22×D8×C23 | 2 |
| C2×#496 | 23 |