Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1112 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C22⋊Dic29 | C2 | semidirect |
| 3. C2×#11745154 | C2 | direct (N × H) |
| 4. C22×C22⋊C4×C29 | C2 | semidirect |
| 6. C24×D29 | C4 | semidirect |
| 12. C22×C22⋊D29 | C4 | semidirect |
| 15. C23×Dic29 | C4 | semidirect |
| 17. C2×C22⋊C4×C29 | C22 | semidirect |
| 19. C2×C22⋊Dic29 | C22 | semidirect |
| 20. #11745154 | C22 | direct (N × H) |
| 32. C23×D29 | C2×C4 | semidirect |
| 42. C2×C22⋊D29 | C2×C4 | semidirect |
| 48. C22×Dic29 | C2×C4 | semidirect |
| 50. C22⋊C4×C29 | C23 | semidirect |
| 52. C22⋊Dic29 | C23 | semidirect |
| 77. C22×D29 | C22×C4 | semidirect |
| 88. C2×Dic29 | C22×C4 | semidirect |
| 101. C22×C29 | #99 | semidirect |
| 118. C22×C22⋊C4 | D29 | semidirect |
| 126. C2×C29 | C2×#99 | semidirect |
| 143. C2×C22⋊C4 | C2×D29 | semidirect |
| 145. C29 | C22×#99 | semidirect |
| 177. C22⋊C4 | C22×D29 | semidirect |
| 229. C22 | #11745154 | direct (N × H) |
| 247. C2 | C2×#11745154 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D29 | 2 |
| C22×C22⋊Dic29 | 2 |
| C2×#11745154 | 2 |
| C22×C22⋊C4×C29 | 2 |
| C22×#99 | 29 |