Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
524 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×D232 | C2 | semidirect |
| 2. #14271727 | C2 | semidirect |
| 3. #14271416 | C2 | semidirect |
| 4. #14271399 | C2 | semidirect |
| 5. #14271201 | C2 | semidirect |
| 6. #14271169 | C2 | semidirect |
| 7. C2×C29×#131 | C2 | semidirect |
| 12. C2×M16×C29 | C22 | semidirect |
| 14. C22×C8×C29 | C22 | semidirect |
| 18. #11745292 | C22 | semidirect |
| 23. #11745169 | C22 | semidirect |
| 24. #11745166 | C22 | semidirect |
| 25. #11745165 | C22 | semidirect |
| 42. C2×C8×C29 | D4 | semidirect |
| 90. C2×#131 | D29 | semidirect |
| 108. C2×M16 | C2×D29 | semidirect |
| 110. C22×C8 | C2×D29 | semidirect |
| 119. C29 | #3058 | semidirect |
| 138. C2×C8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| #14271727 | 2 |
| #14271416 | 2 |
| #14271399 | 2 |
| #14271201 | 2 |
| #14271169 | 2 |
| C2×C29×#131 | 2 |
| #3058 | 29 |