Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11745266 | C2 | semidirect |
| 2. #14271593 | C2 | direct (N × H) |
| 3. C2×#11745177 | C2 | semidirect |
| 4. C2×#11745175 | C2 | semidirect |
| 5. C2×#11745176 | C2 | semidirect |
| 6. C2×#11745174 | C2 | semidirect |
| 7. C22×#90768 | C2 | semidirect |
| 8. C2×C29×#135 | C2 | semidirect |
| 12. C29×#135 | C22 | semidirect |
| 19. #11745266 | C22 | semidirect |
| 22. #11745177 | C22 | semidirect |
| 23. #11745176 | C22 | semidirect |
| 24. #11745175 | C22 | semidirect |
| 25. #11745174 | C22 | semidirect |
| 28. C2×#90768 | C22 | semidirect |
| 96. C2×#135 | D29 | semidirect |
| 105. C2×C29 | #508 | semidirect |
| 113. #135 | C2×D29 | semidirect |
| 128. C29 | C2×#508 | semidirect |
| 197. C2 | #14271593 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| #14271593 | 2 |
| C2×#11745177 | 2 |
| C2×#11745175 | 2 |
| C2×#11745176 | 2 |
| C2×#11745174 | 2 |
| C22×#90768 | 2 |
| C2×C29×#135 | 2 |
| C2×#508 | 29 |