Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
380 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 95 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. #14271021 | C2 | semidirect |
| 4. #14270929 | C2 | semidirect |
| 7. C23×Dic29 | C4 | semidirect |
| 10. C2×C22⋊Dic29 | C4 | semidirect |
| 15. C2×C4⋊Dic29 | C4 | semidirect |
| 17. C2×C4×Dic29 | C4 | semidirect |
| 56. C23×C29 | C4⋊C4 | semidirect |
| 69. C2×C4×C29 | C4⋊C4 | semidirect |
| 111. Dic29 | #99 | semidirect |
| 140. C29 | #1799 | semidirect |
| 176. C23 | #90779 | semidirect |
| 205. C2×C4 | #90779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic29 | 2 |
| C2×#11745182 | 2 |
| #14271021 | 2 |
| #14270929 | 2 |
| C2×C29×#99 | 2 |
| #1799 | 29 |