Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×C4×Dic74 | C2 | semidirect |
| 3. #14557633 | C2 | direct (N × H) |
| 4. C2×#11924469 | C2 | semidirect |
| 5. C2×#11924459 | C2 | semidirect |
| 7. C2×#11924447 | C2 | semidirect |
| 10. C2×#10596940 | C4 | semidirect |
| 15. C4×Dic74 | C22 | semidirect |
| 19. #11924469 | C22 | semidirect |
| 20. #11924459 | C22 | semidirect |
| 22. #11924447 | C22 | semidirect |
| 45. C2×Dic74 | C2×C4 | semidirect |
| 52. #10596940 | C2×C4 | semidirect |
| 58. C2×#64436 | C2×C4 | semidirect |
| 86. Dic74 | C22×C4 | semidirect |
| 88. #64436 | C22×C4 | semidirect |
| 107. C2×C37 | #440 | semidirect |
| 119. C37 | C2×#440 | semidirect |
| 217. C2 | #14557633 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596940 | 2 |
| C2×C4×Dic74 | 2 |
| #14557633 | 2 |
| C2×#11924469 | 2 |
| C2×#11924459 | 2 |
| C2×#11924457 | 2 |
| C2×#11924447 | 2 |
| C2×C4×D4×C37 | 2 |
| C2×#440 | 37 |