Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
618 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 90 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×#11745224 | C2 | semidirect |
| 2. #14272134 | C2 | semidirect |
| 3. C4×C22⋊#1181 | C2 | semidirect |
| 5. C22×D4×C29 | C4 | semidirect |
| 11. C2×#90807 | C4 | semidirect |
| 14. C22×Dic58 | C4 | semidirect |
| 16. C2×C4×#1181 | C22 | semidirect |
| 17. C2×#90796 | C22 | semidirect |
| 70. D4×C29 | C22⋊C4 | semidirect |
| 89. Dic58 | C22⋊C4 | semidirect |
| 98. C22×C29 | #104 | semidirect |
| 131. C22×D4 | #1181 | semidirect |
| 141. C29 | #1789 | semidirect |
| 192. D4 | C22⋊#1181 | semidirect |
| 224. C22 | #11745224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745224 | 2 |
| #14272134 | 2 |
| C4×C22⋊#1181 | 2 |
| C22×#90807 | 2 |
| #1789 | 29 |