Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
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×#11924591 | C2 | semidirect |
| 4. C2×C4×#64438 | C2 | semidirect |
| 5. #14558399 | C2 | semidirect |
| 6. #14558399 | C2 | semidirect |
| 10. C2×#10596957 | C4 | semidirect |
| 15. C22⋊#64438 | C4 | semidirect |
| 70. C2×C4×C37 | M16 | semidirect |
| 83. C2×Dic37 | M16 | semidirect |
| 93. #64438 | C22⋊C4 | semidirect |
| 133. C37 | #1753 | semidirect |
| 215. C2×C4 | #10596957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596957 | 2 |
| C2×C22⋊#64438 | 2 |
| C2×#11924591 | 2 |
| C2×C4×#64438 | 2 |
| #14558399 | 2 |
| C22⋊C4×Dic37 | 2 |
| #1753 | 37 |