Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
408 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×#11745182 | C2 | semidirect |
| 3. C2×#11745154 | C2 | semidirect |
| 4. C2×#11745154 | C2 | semidirect |
| 5. #14271021 | C2 | semidirect |
| 6. C22⋊C4×Dic29 | C2 | semidirect |
| 7. C2×C29×#99 | C2 | semidirect |
| 9. C22×C22⋊D29 | C4 | semidirect |
| 14. C2×C22⋊Dic29 | C4 | semidirect |
| 21. C2×#90781 | C4 | semidirect |
| 23. C2×#90779 | C4 | semidirect |
| 65. C22⋊C4×C29 | D4 | semidirect |
| 71. C22⋊Dic29 | D4 | semidirect |
| 172. Dic29 | #99 | semidirect |
| 177. C2×#99 | D29 | semidirect |
| 214. C29 | #1964 | semidirect |
| 260. C22⋊C4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745301 | 2 |
| C2×#11745182 | 2 |
| C2×#11745154 | 2 |
| #14271021 | 2 |
| C22⋊C4×Dic29 | 2 |
| C2×C29×#99 | 2 |
| #1964 | 29 |