Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1104 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 2. C2×#11745254 | C2 | semidirect |
| 3. C2×#11745234 | C2 | semidirect |
| 4. #14271066 | C2 | semidirect |
| 5. #14271065 | C2 | semidirect |
| 6. #14271064 | C2 | semidirect |
| 7. #14271063 | C2 | semidirect |
| 8. #14271018 | C2 | semidirect |
| 9. C29×#390 | C2 | semidirect |
| 15. C2×D4×D29 | C4 | semidirect |
| 18. C2×C4⋊C4×C29 | C22 | semidirect |
| 19. C2×C22⋊C4×C29 | C22 | semidirect |
| 20. C2×C42×C29 | C22 | semidirect |
| 21. C2×C22⋊Dic29 | C22 | semidirect |
| 24. C2×#90781 | C22 | semidirect |
| 25. C2×#90781 | C22 | semidirect |
| 26. C2×C4⋊Dic29 | C22 | semidirect |
| 27. C2×#90779 | C22 | semidirect |
| 28. C2×C4×Dic29 | C22 | semidirect |
| 29. C2×C4×Dic29 | C22 | semidirect |
| 111. C4×D29 | C22⋊C4 | semidirect |
| 147. #390 | D29 | semidirect |
| 169. C2×C4⋊C4 | C2×D29 | semidirect |
| 175. C2×C22⋊C4 | C2×D29 | semidirect |
| 178. C2×C42 | C2×D29 | semidirect |
| 179. C29 | #2309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D29 | 2 |
| C2×#11745254 | 2 |
| C2×#11745234 | 2 |
| #14271066 | 2 |
| #14271065 | 2 |
| #14271064 | 2 |
| #14271063 | 2 |
| #14271018 | 2 |
| C29×#390 | 2 |
| #2309 | 29 |