Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
244 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 7. C29×#125 | C4 | semidirect |
| 10. #11745250 | C4 | semidirect |
| 13. #11745232 | C4 | semidirect |
| 22. C4×#1181 | Q8 | semidirect |
| 70. #125 | #1181 | semidirect |
| 78. C29 | #1995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272167 | 2 |
| #14272099 | 2 |
| #14272033 | 2 |
| #14271719 | 2 |
| #1995 | 29 |