Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
396 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 105 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. #14271187 | C2 | semidirect |
| 2. C2×#11745181 | C2 | semidirect |
| 3. C4×#90777 | C2 | semidirect |
| 32. #90777 | D4 | semidirect |
| 61. C4×C29 | #100 | semidirect |
| 85. C29 | #1965 | semidirect |
| 129. C4 | #11745181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271187 | 2 |
| C2×#11745181 | 2 |
| C4×#90777 | 2 |
| C2×C29×#127 | 2 |
| #1965 | 29 |