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. #41×Dic29 | C2 | semidirect |
| 2. #14271275 | C2 | semidirect |
| 3. #14271270 | C2 | semidirect |
| 4. #14271264 | C2 | semidirect |
| 5. #14271201 | C2 | semidirect |
| 6. #14271159 | C2 | semidirect |
| 7. C2×#11745163 | 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 |
| 99. #135 | Dic29 | semidirect |
| 118. C29 | #2943 | semidirect |
| 120. #41 | C2×Dic29 | semidirect |
| 128. Q16 | C2×Dic29 | semidirect |
| 129. SD16 | C2×Dic29 | semidirect |
| 130. D8 | C2×Dic29 | semidirect |
| 133. C2×C8 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic29 | 2 |
| #14271275 | 2 |
| #14271270 | 2 |
| #14271264 | 2 |
| #14271201 | 2 |
| #14271159 | 2 |
| C2×#11745163 | 2 |
| C2×C29×#135 | 2 |
| #2943 | 29 |