Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#11745306 | C2 | semidirect |
| 4. #14271366 | C2 | direct (N × H) |
| 5. C2×#11745162 | C2 | semidirect |
| 6. C2×#11745164 | C2 | semidirect |
| 7. C2×#11745183 | C2 | semidirect |
| 18. #11745306 | C22 | semidirect |
| 28. #11745183 | C22 | semidirect |
| 29. #11745164 | C22 | semidirect |
| 30. #11745162 | C22 | semidirect |
| 88. C2×Dic29 | SD16 | semidirect |
| 112. Dic29 | C2×SD16 | semidirect |
| 122. C2×C29 | #461 | semidirect |
| 148. C29 | C2×#461 | semidirect |
| 231. C2 | #14271366 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90783 | 2 |
| C2×#11745306 | 2 |
| C2×D4×Dic29 | 2 |
| #14271366 | 2 |
| C2×#11745162 | 2 |
| C2×#11745164 | 2 |
| C2×#11745183 | 2 |
| C22×SD16×C29 | 2 |
| C2×#461 | 29 |