Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1160 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1160 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. #14271042 | C2 | semidirect |
| 4. #14271040 | C2 | semidirect |
| 5. #14271024 | C2 | semidirect |
| 6. #14271018 | C2 | semidirect |
| 7. C22×C22⋊C4×C29 | C2 | semidirect |
| 10. C23×C4×C29 | C22 | semidirect |
| 13. C22×C22⋊D29 | C4 | semidirect |
| 17. C23×Dic29 | C22 | semidirect |
| 20. C2×C22⋊C4×C29 | C22 | semidirect |
| 23. C2×C22⋊Dic29 | C22 | semidirect |
| 24. C2×#90781 | C22 | semidirect |
| 25. #11745179 | C22 | semidirect |
| 36. C23×D29 | C2×C4 | semidirect |
| 46. C2×C22⋊D29 | C2×C4 | semidirect |
| 47. C2×C22⋊D29 | C2×C4 | semidirect |
| 52. C22×Dic29 | C2×C4 | semidirect |
| 66. C23×C29 | C22⋊C4 | semidirect |
| 125. C22×C22⋊C4 | D29 | semidirect |
| 147. C23×C4 | C2×D29 | semidirect |
| 154. C2×C22⋊C4 | C2×D29 | semidirect |
| 156. C29 | #2308 | semidirect |
| 205. C23 | #90781 | semidirect |
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 |
| #14271042 | 2 |
| #14271040 | 2 |
| #14271024 | 2 |
| #14271018 | 2 |
| C22×C22⋊C4×C29 | 2 |
| #2308 | 29 |