Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745271 | C2 | semidirect |
| 3. #14271734 | C2 | semidirect |
| 4. #14271421 | C2 | semidirect |
| 5. #14271409 | C2 | semidirect |
| 6. #14271404 | C2 | semidirect |
| 7. #14271392 | C2 | semidirect |
| 8. #14271205 | C2 | semidirect |
| 9. #14271160 | C2 | semidirect |
| 10. C2×#11745164 | C2 | semidirect |
| 11. C2×C29×#131 | C2 | semidirect |
| 64. M16×C29 | D4 | semidirect |
| 139. C2×#131 | D29 | semidirect |
| 186. C29 | #3063 | semidirect |
| 210. M16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745271 | 2 |
| #14271741 | 2 |
| #14271734 | 2 |
| #14271421 | 2 |
| #14271409 | 2 |
| #14271404 | 2 |
| #14271392 | 2 |
| #14271205 | 2 |
| #14271160 | 2 |
| C2×#11745164 | 2 |
| C2×C29×#131 | 2 |
| #3063 | 29 |