Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
348 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#11745218 | C2 | semidirect |
| 4. C2×C4×#6599 | C2 | semidirect |
| 5. #14272029 | C2 | semidirect |
| 6. #14272029 | C2 | semidirect |
| 11. C2×#90800 | C4 | semidirect |
| 20. C22⋊#6599 | C4 | semidirect |
| 70. C2×C4×C29 | M16 | semidirect |
| 83. C2×Dic29 | M16 | semidirect |
| 93. #6599 | C22⋊C4 | semidirect |
| 150. C29 | #1753 | semidirect |
| 215. C2×C4 | #90800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90800 | 2 |
| C2×C22⋊#6599 | 2 |
| C2×#11745218 | 2 |
| C2×C4×#6599 | 2 |
| #14272029 | 2 |
| C22⋊C4×Dic29 | 2 |
| #1753 | 29 |