Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 156 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. #14272193 | C2 | semidirect |
| 2. #14272183 | C2 | semidirect |
| 3. #14272134 | C2 | semidirect |
| 4. D29⋊(C22⋊C8) | C2 | semidirect |
| 9. C2×#90796 | C22 | semidirect |
| 10. C2×D29⋊C8 | C22 | semidirect |
| 18. #11745220 | C22 | semidirect |
| 19. #11745219 | C22 | semidirect |
| 20. #11745219 | C22 | semidirect |
| 21. #11745218 | C22 | semidirect |
| 51. C22×D29 | M16 | semidirect |
| 117. C29 | #2973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272193 | 2 |
| #14272183 | 2 |
| #14272134 | 2 |
| D29⋊(C22⋊C8) | 2 |
| C2×#11745255 | 2 |
| #2973 | 29 |