Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
412 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 129 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. C4×C22⋊Dic29 | C2 | semidirect |
| 3. #14270930 | C2 | semidirect |
| 6. C23×C4×C29 | C4 | semidirect |
| 10. C2×C4⋊C4×C29 | C4 | semidirect |
| 11. C2×C22⋊C4×C29 | C4 | semidirect |
| 13. C2×C42×C29 | C4 | semidirect |
| 16. #11745182 | C4 | direct (N × H) |
| 41. C22⋊Dic29 | C2×C4 | semidirect |
| 49. C23×C29 | C42 | semidirect |
| 67. C2×C4×C29 | C42 | semidirect |
| 95. C4×C29 | #99 | semidirect |
| 109. C23×C4 | Dic29 | semidirect |
| 113. C2×C4⋊C4 | Dic29 | semidirect |
| 115. C2×C22⋊C4 | Dic29 | semidirect |
| 118. C2×C42 | Dic29 | semidirect |
| 121. C29 | C4×#99 | semidirect |
| 153. C23 | C4×Dic29 | semidirect |
| 174. C2×C4 | C4×Dic29 | semidirect |
| 199. C4 | #11745182 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745182 | 2 |
| C4×C22⋊Dic29 | 2 |
| #14270930 | 2 |
| C2×C4×D4×C29 | 2 |
| C4×#99 | 29 |