Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
374 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #14271036 | C2 | semidirect |
| 4. #14270929 | C2 | semidirect |
| 18. #11745182 | C4 | semidirect |
| 42. C22⋊Dic29 | C2×C4 | semidirect |
| 53. C23×C29 | C4⋊C4 | semidirect |
| 71. C2×C4×C29 | C4⋊C4 | semidirect |
| 132. C29 | #1867 | semidirect |
| 166. C23 | #90779 | semidirect |
| 193. C2×C4 | #90779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271638 | 2 |
| C2×#11745182 | 2 |
| #14271036 | 2 |
| #14270929 | 2 |
| C29×#386 | 2 |
| #1867 | 29 |