Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
792 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 218 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. C22×#10596957 | C2 | semidirect |
| 2. C23×#64438 | C2 | semidirect |
| 3. #14558506 | C2 | direct (N × H) |
| 4. C2×#11924593 | C2 | semidirect |
| 5. C2×C22⋊#64438 | C2 | semidirect |
| 8. C2×#10596957 | C22 | semidirect |
| 12. C22×#64438 | C22 | semidirect |
| 13. #11924593 | C22 | semidirect |
| 14. C22⋊#64438 | C22 | semidirect |
| 118. C2×C37 | #408 | semidirect |
| 128. C37 | C2×#408 | semidirect |
| 240. C2 | #14558506 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596957 | 2 |
| C23×#64438 | 2 |
| #14558506 | 2 |
| C2×#11924593 | 2 |
| C2×C22⋊#64438 | 2 |
| C22×#10596964 | 2 |
| C2×#408 | 37 |