Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#11924562 | C2 | semidirect |
| 2. C2×#11924542 | C2 | semidirect |
| 3. #14557800 | C2 | direct (N × H) |
| 4. C2×#11924472 | C2 | semidirect |
| 5. C2×#11924453 | C2 | semidirect |
| 6. C22×D8×C37 | C2 | semidirect |
| 9. #11924562 | C22 | semidirect |
| 13. #11924542 | C22 | semidirect |
| 18. #11924472 | C22 | semidirect |
| 19. #11924453 | C22 | semidirect |
| 24. C2×D8×C37 | C22 | semidirect |
| 106. C2×C37 | #472 | semidirect |
| 110. C22×D8 | D37 | semidirect |
| 115. C37 | C2×#472 | semidirect |
| 125. C2×D8 | C2×D37 | semidirect |
| 215. C2 | #14557800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924562 | 2 |
| C2×#11924542 | 2 |
| #14557800 | 2 |
| C2×#11924472 | 2 |
| C2×#11924453 | 2 |
| C22×D8×C37 | 2 |
| C2×#472 | 37 |