Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 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. C22×#90807 | C2 | semidirect |
| 2. C2×#11745278 | C2 | semidirect |
| 3. #14271676 | C2 | semidirect |
| 4. #14271322 | C2 | semidirect |
| 5. #14271318 | C2 | semidirect |
| 6. #14271309 | C2 | semidirect |
| 7. #14271304 | C2 | semidirect |
| 8. #14271297 | C2 | semidirect |
| 9. #14271156 | C2 | semidirect |
| 10. C22⋊C8×D29 | C2 | semidirect |
| 11. C29×#450 | C2 | semidirect |
| 15. C2×#90809 | C22 | semidirect |
| 23. C2×SD16×C29 | C22 | semidirect |
| 25. #11745308 | C22 | semidirect |
| 26. C2×#90785 | C22 | semidirect |
| 27. C2×#90782 | C22 | semidirect |
| 30. C2×#90773 | C22 | semidirect |
| 31. C2×C8×D29 | C22 | semidirect |
| 32. #11745257 | C22 | semidirect |
| 35. #11745254 | C22 | semidirect |
| 38. C29×#102 | C22 | semidirect |
| 40. #11745180 | C22 | semidirect |
| 42. #11745168 | C22 | semidirect |
| 43. #11745164 | C22 | semidirect |
| 44. #11745158 | C22 | semidirect |
| 67. #90807 | D4 | semidirect |
| 148. C22×C29 | #135 | semidirect |
| 173. #450 | D29 | semidirect |
| 201. C2×SD16 | C2×D29 | semidirect |
| 216. #102 | C2×D29 | semidirect |
| 220. C29 | #3002 | semidirect |
| 333. C22 | #11745278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90807 | 2 |
| C2×#11745278 | 2 |
| #14271676 | 2 |
| #14271322 | 2 |
| #14271318 | 2 |
| #14271309 | 2 |
| #14271304 | 2 |
| #14271297 | 2 |
| #14271156 | 2 |
| C22⋊C8×D29 | 2 |
| C29×#450 | 2 |
| #3002 | 29 |