Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#11745263 | C2 | semidirect |
| 3. #14271732 | C2 | semidirect |
| 4. #14271417 | C2 | semidirect |
| 5. #14271400 | C2 | semidirect |
| 6. #14271167 | C2 | semidirect |
| 7. C29×#427 | C2 | semidirect |
| 17. C2×#90772 | C22 | semidirect |
| 18. C2×C8×D29 | C22 | semidirect |
| 19. #11745257 | C22 | semidirect |
| 23. C29×#107 | C22 | semidirect |
| 24. C29×#106 | C22 | semidirect |
| 25. #11745157 | C22 | semidirect |
| 39. C2×C8×C29 | D4 | semidirect |
| 94. #427 | D29 | semidirect |
| 116. #107 | C2×D29 | semidirect |
| 117. #106 | C2×D29 | semidirect |
| 119. C29 | #3058 | semidirect |
| 139. C2×C8 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| C2×#11745263 | 2 |
| #14271732 | 2 |
| #14271417 | 2 |
| #14271400 | 2 |
| #14271167 | 2 |
| C29×#427 | 2 |
| #3058 | 29 |