Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 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×#11745362 | C2 | semidirect |
| 2. C2×#11745312 | C2 | semidirect |
| 3. #14271741 | C2 | semidirect |
| 4. #14271324 | C2 | semidirect |
| 5. #14271317 | C2 | semidirect |
| 6. #14271307 | C2 | semidirect |
| 7. #14271300 | C2 | semidirect |
| 8. #14271165 | C2 | semidirect |
| 9. C2×#11745183 | C2 | semidirect |
| 10. #14271131 | C2 | semidirect |
| 11. C2×C29×#137 | C2 | semidirect |
| 49. C2×Q8×C29 | D4 | semidirect |
| 71. #90805 | D4 | semidirect |
| 164. C2×#137 | D29 | semidirect |
| 214. C29 | #3013 | semidirect |
| 233. C2×Q8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745362 | 2 |
| C2×#11745312 | 2 |
| #14271741 | 2 |
| #14271324 | 2 |
| #14271317 | 2 |
| #14271307 | 2 |
| #14271300 | 2 |
| #14271165 | 2 |
| C2×#11745183 | 2 |
| #14271131 | 2 |
| C2×C29×#137 | 2 |
| #3013 | 29 |