Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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. #14271054 | C2 | semidirect |
| 3. #14271052 | C2 | semidirect |
| 4. #14271021 | C2 | semidirect |
| 6. C4×C22⋊Dic29 | C2 | semidirect |
| 7. C4×C22⋊C4×C29 | C2 | semidirect |
| 12. C2×C42×C29 | C22 | semidirect |
| 14. C2×#90781 | C4 | semidirect |
| 19. C2×#90779 | C22 | semidirect |
| 20. C2×C4×Dic29 | C22 | semidirect |
| 21. C29×#95 | C22 | semidirect |
| 22. #11745179 | C22 | semidirect |
| 23. #11745179 | C22 | semidirect |
| 100. C4×C22⋊C4 | D29 | semidirect |
| 119. C2×C42 | C2×D29 | semidirect |
| 122. #95 | C2×D29 | semidirect |
| 123. C29 | #2312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90781 | 2 |
| #14271054 | 2 |
| #14271052 | 2 |
| #14271021 | 2 |
| #14271018 | 2 |
| C4×C22⋊Dic29 | 2 |
| C4×C22⋊C4×C29 | 2 |
| #2312 | 29 |