Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
346 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 60 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. #14272135 | C2 | semidirect |
| 2. C4×C22⋊#1181 | C2 | semidirect |
| 3. #14272015 | C2 | semidirect |
| 4. #14272014 | C2 | semidirect |
| 7. C2×D4×D29 | C4 | semidirect |
| 12. C29×#121 | C4 | semidirect |
| 15. #11745292 | C4 | semidirect |
| 17. C4⋊C4×D29 | C4 | semidirect |
| 20. (C2×#1181)⋊C4 | C22 | semidirect |
| 22. #11745219 | C22 | semidirect |
| 137. #121 | #1181 | semidirect |
| 145. C29 | #1507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272135 | 2 |
| C4×C22⋊#1181 | 2 |
| #14272015 | 2 |
| #14272014 | 2 |
| #121×D29 | 2 |
| #1507 | 29 |