Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11745304 | C2 | semidirect |
| 3. #14271641 | C2 | semidirect |
| 4. #14271383 | C2 | semidirect |
| 5. #14271361 | C2 | semidirect |
| 6. #14271189 | C2 | semidirect |
| 7. #14271168 | C2 | semidirect |
| 8. #14271160 | C2 | semidirect |
| 9. C22×SD16×C29 | C2 | semidirect |
| 18. Q8×Dic29 | C22 | semidirect |
| 19. C2×#90785 | C22 | semidirect |
| 21. C2×#90784 | C22 | semidirect |
| 30. #11745169 | C22 | semidirect |
| 31. #11745164 | C22 | semidirect |
| 32. #11745162 | C22 | semidirect |
| 36. C2×Q8×C29 | D4 | semidirect |
| 113. C22×SD16 | D29 | semidirect |
| 149. C29 | #3043 | semidirect |
| 156. 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×#11745304 | 2 |
| #14271730 | 2 |
| #14271641 | 2 |
| #14271383 | 2 |
| #14271361 | 2 |
| #14271189 | 2 |
| #14271168 | 2 |
| #14271160 | 2 |
| C22×SD16×C29 | 2 |
| #3043 | 29 |