Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
440 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 135 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. #13092970 | C2 | semidirect |
| 3. #13092720 | C2 | semidirect |
| 4. #13092716 | C2 | semidirect |
| 5. #13092706 | C2 | semidirect |
| 6. #13092696 | C2 | semidirect |
| 7. #13092457 | C2 | semidirect |
| 8. #13092440 | C2 | semidirect |
| 11. C23×#428 | C2 | semidirect |
| 25. #10625061 | C22 | semidirect |
| 26. #10625061 | C22 | semidirect |
| 27. #10625059 | C22 | semidirect |
| 28. #10625059 | C22 | semidirect |
| 33. C23×#107 | C22 | semidirect |
| 34. C23×#106 | C22 | semidirect |
| 37. Dic23⋊C8 | C22 | semidirect |
| 38. Dic23⋊C8 | C22 | semidirect |
| 41. #10624990 | C22 | semidirect |
| 42. #10624989 | C22 | semidirect |
| 50. C2×D92 | Q8 | semidirect |
| 141. #428 | D23 | semidirect |
| 172. #107 | C2×D23 | semidirect |
| 174. #106 | C2×D23 | semidirect |
| 181. C23 | #3077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092970 | 2 |
| C2×#10625064 | 2 |
| #13092720 | 2 |
| #13092716 | 2 |
| #13092706 | 2 |
| #13092696 | 2 |
| #13092457 | 2 |
| #13092440 | 2 |
| #13092423 | 2 |
| #13092421 | 2 |
| C23×#428 | 2 |
| #3077 | 23 |