Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. M16×#1181 | C2 | semidirect |
| 4. #14272042 | C2 | semidirect |
| 15. #11745229 | C4 | semidirect |
| 18. C29×#100 | C4 | semidirect |
| 19. #11745181 | C4 | semidirect |
| 20. #11745171 | C4 | semidirect |
| 35. #90800 | C2×C4 | semidirect |
| 41. M16×C29 | C2×C4 | semidirect |
| 42. #90777 | C2×C4 | semidirect |
| 87. #1181 | #100 | direct (N × H) |
| 114. #100 | #1181 | direct (N × H) |
| 117. C29 | C4×#100 | semidirect |
| 135. M16 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#1181 | 2 |
| D29⋊#100 | 2 |
| M16×#1181 | 2 |
| #14272042 | 2 |
| #100×D29 | 2 |
| C4×#100 | 29 |