Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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. #14271220 | C2 | semidirect |
| 3. #14270899 | C2 | semidirect |
| 5. C4×C4⋊C4×C29 | C2 | semidirect |
| 14. #11745237 | C4 | semidirect |
| 15. C4×D116 | C4 | semidirect |
| 17. #11745232 | C4 | semidirect |
| 18. C4×Dic58 | C4 | semidirect |
| 95. C4×C4⋊C4 | D29 | semidirect |
| 121. C29 | #1509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271697 | 2 |
| #14271220 | 2 |
| #14270899 | 2 |
| #14270896 | 2 |
| C4×C4⋊C4×C29 | 2 |
| #1509 | 29 |