Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
528 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 528 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. #14271638 | C2 | semidirect |
| 2. #14271275 | C2 | semidirect |
| 3. D8×Dic29 | C2 | semidirect |
| 4. #14271201 | C2 | semidirect |
| 5. #14271168 | C2 | semidirect |
| 6. #14271118 | C2 | semidirect |
| 9. C2×D8×C29 | C4 | semidirect |
| 15. D4×Dic29 | C22 | semidirect |
| 19. #11745180 | C22 | semidirect |
| 20. #11745166 | C22 | semidirect |
| 21. #11745165 | C22 | semidirect |
| 22. #11745163 | C22 | semidirect |
| 23. C8×Dic29 | C22 | semidirect |
| 27. C2×D4×C29 | C2×C4 | semidirect |
| 31. D8×C29 | C2×C4 | semidirect |
| 32. D8×C29 | C2×C4 | semidirect |
| 33. C2×C8×C29 | C2×C4 | semidirect |
| 86. C2×D8 | Dic29 | semidirect |
| 101. C29 | #2948 | semidirect |
| 105. C2×D4 | C2×Dic29 | semidirect |
| 109. D8 | C2×Dic29 | semidirect |
| 110. D8 | C2×Dic29 | semidirect |
| 113. C2×C8 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271638 | 2 |
| #14271275 | 2 |
| D8×Dic29 | 2 |
| #14271201 | 2 |
| #14271168 | 2 |
| #14271118 | 2 |
| C22×D8×C29 | 2 |
| #2948 | 29 |