Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
992 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×#90777 | C2 | semidirect |
| 3. C2×#11745171 | C2 | direct (N × H) |
| 4. C22×M16×C29 | C2 | semidirect |
| 14. C2×M16×C29 | C22 | semidirect |
| 17. C2×#90777 | C22 | semidirect |
| 19. #11745171 | C22 | direct (N × H) |
| 41. M16×C29 | C23 | semidirect |
| 44. #90777 | C23 | semidirect |
| 74. C22×C29 | #100 | semidirect |
| 88. C22×M16 | D29 | semidirect |
| 92. C2×C29 | C2×#100 | semidirect |
| 106. C2×M16 | C2×D29 | semidirect |
| 110. C29 | C22×#100 | semidirect |
| 134. M16 | C22×D29 | semidirect |
| 168. C22 | #11745171 | direct (N × H) |
| 179. C2 | C2×#11745171 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D116 | 2 |
| C22×#90777 | 2 |
| C2×#11745171 | 2 |
| C22×M16×C29 | 2 |
| C22×#100 | 29 |