Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 269 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. #14557573 | C2 | direct (N × H) |
| 4. C2×#11924469 | C2 | semidirect |
| 5. C2×#11924467 | C2 | semidirect |
| 7. C2×#10596934 | C4 | semidirect |
| 16. #11924469 | C22 | semidirect |
| 17. #11924467 | C22 | semidirect |
| 45. #10596934 | C2×C4 | semidirect |
| 46. C2×#64436 | C2×C4 | semidirect |
| 69. #64436 | C22×C4 | semidirect |
| 87. C2×C37 | #428 | semidirect |
| 97. C37 | C2×#428 | semidirect |
| 177. C2 | #14557573 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596934 | 2 |
| C2×#11924495 | 2 |
| #14557573 | 2 |
| C2×#11924469 | 2 |
| C2×#11924467 | 2 |
| C22×C4⋊C4×C37 | 2 |
| C2×#428 | 37 |