Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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×#11745310 | C2 | semidirect |
| 2. #14271646 | C2 | semidirect |
| 3. #14271168 | C2 | semidirect |
| 4. #14271164 | C2 | semidirect |
| 5. #14271159 | C2 | semidirect |
| 6. C2×#11745180 | C2 | semidirect |
| 9. C29×H(5,𝔽2) | C4 | semidirect |
| 18. #11745288 | C22 | semidirect |
| 19. C2×C4⋊Dic29 | C22 | semidirect |
| 20. C2×#90777 | C22 | semidirect |
| 21. C22×#6597 | C22 | semidirect |
| 22. #11745183 | C22 | semidirect |
| 23. #11745183 | C22 | semidirect |
| 24. #11745180 | C22 | semidirect |
| 25. #11745180 | C22 | semidirect |
| 26. #11745180 | C22 | semidirect |
| 31. #41×C29 | C2×C4 | semidirect |
| 39. C2×D4×C29 | C2×C4 | semidirect |
| 106. H(5,𝔽2) | Dic29 | semidirect |
| 124. C29 | #2897 | semidirect |
| 129. #41 | C2×Dic29 | semidirect |
| 137. C2×D4 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745310 | 2 |
| #14271646 | 2 |
| #14271168 | 2 |
| #14271164 | 2 |
| #14271159 | 2 |
| C2×#11745180 | 2 |
| C2×C29×H(5,𝔽2) | 2 |
| #2897 | 29 |