Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14271694 | C2 | semidirect |
| 2. #14271564 | C2 | semidirect |
| 3. #14271546 | C2 | semidirect |
| 4. #14271516 | C2 | semidirect |
| 5. #14271404 | C2 | semidirect |
| 6. #14271390 | C2 | semidirect |
| 7. #14271257 | C2 | semidirect |
| 8. #14271254 | C2 | semidirect |
| 9. D8×Dic29 | C2 | semidirect |
| 10. C2×C8×Dic29 | C2 | semidirect |
| 157. C29 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271694 | 2 |
| #14271564 | 2 |
| #14271546 | 2 |
| #14271516 | 2 |
| #14271404 | 2 |
| #14271390 | 2 |
| #14271257 | 2 |
| #14271254 | 2 |
| D8×Dic29 | 2 |
| C2×C8×Dic29 | 2 |
| C29×#466 | 2 |
| #3168 | 29 |