Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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. #14271641 | C2 | semidirect |
| 3. #14271264 | C2 | semidirect |
| 4. SD16×Dic29 | C2 | semidirect |
| 5. #14271201 | C2 | semidirect |
| 6. #14271172 | C2 | semidirect |
| 8. #14271118 | C2 | semidirect |
| 12. C2×SD16×C29 | C4 | semidirect |
| 18. Q8×Dic29 | C22 | semidirect |
| 26. #11745183 | C22 | semidirect |
| 28. #11745166 | C22 | semidirect |
| 29. #11745165 | C22 | semidirect |
| 30. #11745163 | C22 | semidirect |
| 31. C8×Dic29 | C22 | semidirect |
| 35. C2×Q8×C29 | C2×C4 | semidirect |
| 44. SD16×C29 | C2×C4 | semidirect |
| 45. SD16×C29 | C2×C4 | semidirect |
| 46. C2×C8×C29 | C2×C4 | semidirect |
| 115. C2×SD16 | Dic29 | semidirect |
| 135. C29 | #2949 | semidirect |
| 139. C2×Q8 | C2×Dic29 | semidirect |
| 148. SD16 | C2×Dic29 | semidirect |
| 149. SD16 | C2×Dic29 | semidirect |
| 152. C2×C8 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271641 | 2 |
| #14271638 | 2 |
| #14271264 | 2 |
| SD16×Dic29 | 2 |
| #14271201 | 2 |
| #14271172 | 2 |
| #14271168 | 2 |
| #14271118 | 2 |
| C22×SD16×C29 | 2 |
| #2949 | 29 |