Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
564 conjugacy classes of subgroups; only the 282 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 282 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. #14272127 | C2 | semidirect |
| 3. C4×#90800 | C2 | semidirect |
| 6. C2×#90800 | C4 | semidirect |
| 16. #11745218 | C22 | semidirect |
| 17. C4×#6599 | C22 | semidirect |
| 27. #90800 | C2×C4 | semidirect |
| 28. C2×#6599 | C2×C4 | semidirect |
| 85. C29 | #2873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90800 | 2 |
| #14272127 | 2 |
| C4×#90800 | 2 |
| C2×#11745239 | 2 |
| #2873 | 29 |