Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 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×#11745270 | C2 | semidirect |
| 2. #14271741 | C2 | semidirect |
| 3. #14271727 | C2 | semidirect |
| 4. #14271416 | C2 | semidirect |
| 5. #14271409 | C2 | semidirect |
| 6. #14271399 | C2 | semidirect |
| 7. #14271392 | C2 | semidirect |
| 8. #14271205 | C2 | semidirect |
| 9. #14271160 | C2 | semidirect |
| 10. C2×#11745169 | C2 | semidirect |
| 11. C2×C29×#131 | C2 | semidirect |
| 17. C2×M16×C29 | C22 | semidirect |
| 19. C22×C8×C29 | C22 | semidirect |
| 28. #11745292 | C22 | semidirect |
| 31. #11745286 | C22 | semidirect |
| 37. #11745169 | C22 | semidirect |
| 38. #11745169 | C22 | semidirect |
| 39. #11745166 | C22 | semidirect |
| 40. #11745165 | C22 | semidirect |
| 41. #11745164 | C22 | semidirect |
| 42. #11745164 | C22 | semidirect |
| 66. M16×C29 | D4 | semidirect |
| 146. C2×#131 | D29 | semidirect |
| 171. C2×M16 | C2×D29 | semidirect |
| 173. C22×C8 | C2×D29 | semidirect |
| 194. C29 | #3062 | semidirect |
| 220. M16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745270 | 2 |
| #14271741 | 2 |
| #14271727 | 2 |
| #14271416 | 2 |
| #14271409 | 2 |
| #14271399 | 2 |
| #14271392 | 2 |
| #14271205 | 2 |
| #14271160 | 2 |
| C2×#11745169 | 2 |
| C2×C29×#131 | 2 |
| #3062 | 29 |