Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 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. C2×#10625120 | C2 | semidirect |
| 2. C22×#67272 | C2 | semidirect |
| 3. #13092981 | C2 | semidirect |
| 4. #13092562 | C2 | semidirect |
| 5. #13092551 | C2 | semidirect |
| 6. #13092422 | C2 | semidirect |
| 7. #13092413 | C2 | semidirect |
| 8. #13092384 | C2 | semidirect |
| 9. C2×C23×H(5,𝔽2) | C2 | semidirect |
| 15. C2×#41×C23 | C22 | semidirect |
| 19. C22×D4×C23 | C22 | semidirect |
| 20. C22×D92 | C22 | semidirect |
| 23. C2×#67274 | C22 | semidirect |
| 27. C2×#67272 | C22 | semidirect |
| 28. C2×#67272 | C22 | semidirect |
| 29. #10625101 | C22 | semidirect |
| 30. #10625097 | C22 | semidirect |
| 31. C2×#67267 | C22 | semidirect |
| 32. C22×C23⋊C8 | C22 | semidirect |
| 33. #10625017 | C22 | semidirect |
| 34. #10625014 | C22 | semidirect |
| 35. #10625014 | C22 | semidirect |
| 36. C22⋊(C23⋊C8) | C22 | semidirect |
| 46. #41×C23 | D4 | semidirect |
| 60. C2×D4×C23 | D4 | semidirect |
| 145. C2×H(5,𝔽2) | D23 | semidirect |
| 166. C2×#41 | C2×D23 | semidirect |
| 171. C22×D4 | C2×D23 | semidirect |
| 188. C23 | #3008 | semidirect |
| 198. #41 | C22⋊D23 | semidirect |
| 217. C2×D4 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625120 | 2 |
| C22×#67272 | 2 |
| #13092981 | 2 |
| #13092562 | 2 |
| #13092551 | 2 |
| #13092422 | 2 |
| #13092413 | 2 |
| #13092384 | 2 |
| C2×C23×H(5,𝔽2) | 2 |
| #3008 | 23 |