Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
444 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 97 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. #14271638 | C2 | semidirect |
| 2. #14271168 | C2 | semidirect |
| 3. C2×#11745181 | C2 | semidirect |
| 4. #14270923 | C2 | semidirect |
| 10. C29×#127 | C4 | semidirect |
| 28. C2×D4×C29 | C2×C4 | semidirect |
| 34. C42×C29 | C2×C4 | semidirect |
| 37. C4⋊Dic29 | D4 | semidirect |
| 98. #127 | Dic29 | semidirect |
| 105. C29 | #1887 | semidirect |
| 116. C2×D4 | C2×Dic29 | semidirect |
| 129. C42 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271638 | 2 |
| #14271168 | 2 |
| C2×#11745181 | 2 |
| #14270923 | 2 |
| C2×C29×#127 | 2 |
| #1887 | 29 |