Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
912 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 290 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 |
|---|---|---|
| 2. C22⋊C4×#1181 | C2 | semidirect |
| 3. C4×C22⋊#1181 | C2 | semidirect |
| 8. C2×C22⋊#1181 | C4 | semidirect |
| 11. C2×C4×#1181 | C22 | semidirect |
| 12. C2×C22⋊C4×C29 | C4 | semidirect |
| 13. C2×C22⋊Dic29 | C4 | semidirect |
| 14. C2×#90781 | C4 | semidirect |
| 15. C22⋊C4×D29 | C4 | semidirect |
| 17. (C2×#1181)⋊C4 | C22 | semidirect |
| 26. C22×#1181 | C2×C4 | semidirect |
| 28. C22×C4×C29 | C2×C4 | semidirect |
| 29. C22×Dic29 | C2×C4 | semidirect |
| 31. C2×C4×D29 | C2×C4 | semidirect |
| 33. C22⋊#1181 | C2×C4 | semidirect |
| 34. C22⋊#1181 | C2×C4 | semidirect |
| 36. C22⋊C4×C29 | C2×C4 | semidirect |
| 37. C22⋊Dic29 | C2×C4 | semidirect |
| 38. #90781 | C2×C4 | semidirect |
| 40. C23×C29 | C42 | semidirect |
| 48. C22×D29 | C42 | semidirect |
| 49. C22×D29 | C42 | semidirect |
| 107. C2×C22⋊C4 | #1181 | semidirect |
| 110. C29 | #2273 | semidirect |
| 125. C22×C4 | C2×#1181 | semidirect |
| 130. C22⋊C4 | C2×#1181 | semidirect |
| 146. C23 | C4×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#1181 | 2 |
| C22⋊C4×#1181 | 2 |
| C4×C22⋊#1181 | 2 |
| C2×C22⋊C4×D29 | 2 |
| #2273 | 29 |