Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
806 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 169 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×#10625120 | C2 | semidirect |
| 2. C2×#10625101 | C2 | semidirect |
| 3. #13092562 | C2 | semidirect |
| 4. #13092556 | C2 | semidirect |
| 5. #13092551 | C2 | semidirect |
| 6. #13092418 | C2 | semidirect |
| 7. #13092381 | C2 | semidirect |
| 8. C22×#41×C23 | C2 | semidirect |
| 13. C2×#41×C23 | C22 | semidirect |
| 14. C22×Q8×C23 | C22 | semidirect |
| 16. C22×D4×C23 | C22 | semidirect |
| 20. C22×D92 | C22 | semidirect |
| 22. C2×#67274 | C22 | semidirect |
| 23. C2×#67272 | C22 | semidirect |
| 27. #10625101 | C22 | semidirect |
| 29. C2×C4⋊Dic23 | C22 | semidirect |
| 30. C2×#67267 | C22 | semidirect |
| 31. #10625017 | C22 | semidirect |
| 32. #10625014 | C22 | semidirect |
| 33. C22⋊(C23⋊C8) | C22 | semidirect |
| 34. C22⋊(C23⋊C8) | C22 | semidirect |
| 43. #41×C23 | D4 | semidirect |
| 95. Q8×C23 | C2×D4 | semidirect |
| 100. D4×C23 | C2×D4 | semidirect |
| 136. C22×C23 | AGL(1,ℤ/8) | semidirect |
| 148. C22×#41 | D23 | semidirect |
| 168. C2×#41 | C2×D23 | semidirect |
| 169. C22×Q8 | C2×D23 | semidirect |
| 173. C22×D4 | C2×D23 | semidirect |
| 190. C23 | #3006 | semidirect |
| 199. #41 | C22⋊D23 | semidirect |
| 251. Q8 | C2×C22⋊D23 | semidirect |
| 260. D4 | C2×C22⋊D23 | semidirect |
| 294. C22 | #10625120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625120 | 2 |
| C2×#10625101 | 2 |
| #13092562 | 2 |
| #13092556 | 2 |
| #13092551 | 2 |
| #13092418 | 2 |
| #13092381 | 2 |
| C22×#41×C23 | 2 |
| #3006 | 23 |