Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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×#11745294 | C2 | semidirect |
| 2. #14271730 | C2 | semidirect |
| 3. #14271638 | C2 | semidirect |
| 4. #14271376 | C2 | semidirect |
| 5. #14271356 | C2 | semidirect |
| 6. #14271189 | C2 | semidirect |
| 7. #14271168 | C2 | semidirect |
| 8. #14271160 | C2 | semidirect |
| 9. C22×D8×C29 | C2 | semidirect |
| 18. #11745302 | C22 | semidirect |
| 20. #11745298 | C22 | semidirect |
| 22. D4×Dic29 | C22 | semidirect |
| 23. C2×#90783 | C22 | semidirect |
| 25. C2×#90782 | C22 | semidirect |
| 29. #11745180 | C22 | semidirect |
| 30. #11745169 | C22 | semidirect |
| 31. #11745164 | C22 | semidirect |
| 32. #11745162 | C22 | semidirect |
| 40. C2×D4×C29 | D4 | semidirect |
| 117. C22×D8 | D29 | semidirect |
| 154. C29 | #3041 | semidirect |
| 168. C2×D4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| #14271730 | 2 |
| #14271638 | 2 |
| #14271376 | 2 |
| #14271356 | 2 |
| #14271189 | 2 |
| #14271168 | 2 |
| #14271160 | 2 |
| C22×D8×C29 | 2 |
| #3041 | 29 |