Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
304 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 62 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. D29⋊(C22⋊C8) | C2 | semidirect |
| 2. C4×C22⋊#1181 | C2 | semidirect |
| 3. #14272016 | C2 | semidirect |
| 4. #14272015 | C2 | semidirect |
| 6. C2×#90805 | C4 | semidirect |
| 11. C29×#117 | C4 | semidirect |
| 12. #11745259 | C4 | semidirect |
| 14. #11745257 | C4 | semidirect |
| 129. #117 | #1181 | semidirect |
| 135. C29 | #1501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D29⋊(C22⋊C8) | 2 |
| C4×C22⋊#1181 | 2 |
| #14272016 | 2 |
| #14272015 | 2 |
| #14271675 | 2 |
| #1501 | 29 |