Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
368 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 77 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×#11745182 | C2 | semidirect |
| 2. #14270956 | C2 | direct (N × H) |
| 5. C22×D4×C29 | C4 | semidirect |
| 8. C29×#127 | C4 | semidirect |
| 10. C2×C42×C29 | C4 | semidirect |
| 13. #11745182 | C22 | semidirect |
| 25. C2×D4×C29 | C2×C4 | semidirect |
| 32. C42×C29 | C2×C4 | semidirect |
| 87. C2×C29 | #353 | semidirect |
| 90. C22×D4 | Dic29 | semidirect |
| 93. #127 | Dic29 | semidirect |
| 96. C2×C42 | Dic29 | semidirect |
| 99. C29 | C2×#353 | semidirect |
| 111. C2×D4 | C2×Dic29 | semidirect |
| 120. C42 | C2×Dic29 | semidirect |
| 169. C2 | #14270956 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745182 | 2 |
| #14270956 | 2 |
| C2×C29×#127 | 2 |
| C2×#353 | 29 |