Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
484 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 484 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. #14271646 | C2 | semidirect |
| 2. #14271264 | C2 | semidirect |
| 3. Q16×Dic29 | C2 | semidirect |
| 4. D8×Dic29 | C2 | semidirect |
| 5. C2×#11745166 | C2 | semidirect |
| 6. #14271164 | C2 | semidirect |
| 7. #14271118 | C2 | semidirect |
| 10. C29×#135 | C4 | semidirect |
| 30. #41×C29 | C2×C4 | semidirect |
| 38. Q16×C29 | C2×C4 | semidirect |
| 39. SD16×C29 | C2×C4 | semidirect |
| 40. D8×C29 | C2×C4 | semidirect |
| 41. C2×C8×C29 | C2×C4 | semidirect |
| 105. #135 | Dic29 | semidirect |
| 124. C29 | #2951 | semidirect |
| 126. #41 | C2×Dic29 | semidirect |
| 134. Q16 | C2×Dic29 | semidirect |
| 135. SD16 | C2×Dic29 | semidirect |
| 136. D8 | C2×Dic29 | semidirect |
| 139. C2×C8 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271646 | 2 |
| #14271264 | 2 |
| Q16×Dic29 | 2 |
| D8×Dic29 | 2 |
| C2×#11745166 | 2 |
| #14271164 | 2 |
| #14271118 | 2 |
| C2×C29×#135 | 2 |
| #2951 | 29 |