Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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. #14557895 | C2 | direct (N × H) |
| 3. C2×#11924459 | C2 | semidirect |
| 5. C2×#11924447 | C2 | semidirect |
| 6. C2×C4⋊Q8×C37 | C2 | semidirect |
| 14. #11924459 | C22 | semidirect |
| 16. #11924447 | C22 | semidirect |
| 19. C4⋊Q8×C37 | C22 | semidirect |
| 83. C2×C37 | #489 | semidirect |
| 88. C2×C4⋊Q8 | D37 | semidirect |
| 94. C37 | C2×#489 | semidirect |
| 100. C4⋊Q8 | C2×D37 | semidirect |
| 171. C2 | #14557895 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924524 | 2 |
| #14557895 | 2 |
| C2×#11924459 | 2 |
| C2×#11924456 | 2 |
| C2×#11924447 | 2 |
| C2×C4⋊Q8×C37 | 2 |
| C2×#489 | 37 |