Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
740 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 170 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×D4×#1181 | C2 | semidirect |
| 2. #14272115 | C2 | semidirect |
| 3. #14272111 | C2 | semidirect |
| 4. #14272107 | C2 | semidirect |
| 5. #14272099 | C2 | semidirect |
| 16. C29×#127 | C4 | semidirect |
| 17. #11745302 | C4 | semidirect |
| 18. #11745302 | C4 | semidirect |
| 19. #11745236 | C4 | semidirect |
| 29. C2×D4×C29 | C2×C4 | semidirect |
| 30. C2×D4×C29 | C2×C4 | semidirect |
| 31. C2×C22⋊D29 | C2×C4 | semidirect |
| 32. C2×C22⋊D29 | C2×C4 | semidirect |
| 36. C2×D116 | C2×C4 | semidirect |
| 37. C2×D116 | C2×C4 | semidirect |
| 44. C4×#1181 | D4 | semidirect |
| 45. C42×C29 | C2×C4 | semidirect |
| 46. C4×Dic29 | C2×C4 | semidirect |
| 47. C4×Dic29 | C2×C4 | semidirect |
| 112. #127 | #1181 | semidirect |
| 122. C29 | #2328 | semidirect |
| 131. C2×D4 | C2×#1181 | semidirect |
| 132. C2×D4 | C2×#1181 | semidirect |
| 147. C42 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#1181 | 2 |
| #14272115 | 2 |
| #14272111 | 2 |
| #14272107 | 2 |
| #14272099 | 2 |
| #127×D29 | 2 |
| #2328 | 29 |