Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
196 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 122 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. #14272051 | C2 | semidirect |
| 3. C4×#90770 | C2 | semidirect |
| 8. #11745214 | C4 | direct (N × H) |
| 25. #90770 | C2×C4 | semidirect |
| 44. C4×C29 | M32 | semidirect |
| 63. C29 | C4×M32 | semidirect |
| 92. C4 | #11745214 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745214 | 2 |
| #14272051 | 2 |
| C4×#90770 | 2 |
| C2×C4×#6597 | 2 |
| C4×M32 | 29 |