Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
608 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 608 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×D148 | C2 | semidirect |
| 3. #14557643 | C2 | direct (N × H) |
| 4. C2×#11924467 | C2 | semidirect |
| 5. C2×#11924457 | C2 | semidirect |
| 6. C2×#11924456 | C2 | semidirect |
| 7. C2×#11924447 | C2 | semidirect |
| 8. C2×C4×D4×C37 | C2 | semidirect |
| 11. C2×#10596939 | C4 | semidirect |
| 16. C4×D148 | C22 | semidirect |
| 19. #11924467 | C22 | semidirect |
| 20. #11924457 | C22 | semidirect |
| 21. #11924456 | C22 | semidirect |
| 22. #11924447 | C22 | semidirect |
| 26. C4×D4×C37 | C22 | semidirect |
| 34. C2×D4×C37 | C2×C4 | semidirect |
| 45. C2×D148 | C2×C4 | semidirect |
| 54. #10596939 | C2×C4 | semidirect |
| 59. C2×#64436 | C2×C4 | semidirect |
| 73. D4×C37 | C22×C4 | semidirect |
| 89. D148 | C22×C4 | semidirect |
| 92. #64436 | C22×C4 | semidirect |
| 114. C2×C37 | #442 | semidirect |
| 121. C2×C4×D4 | D37 | semidirect |
| 127. C37 | C2×#442 | semidirect |
| 139. C4×D4 | C2×D37 | semidirect |
| 157. C2×D4 | C4×D37 | semidirect |
| 195. D4 | C2×C4×D37 | semidirect |
| 233. C2 | #14557643 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596939 | 2 |
| C2×C4×D148 | 2 |
| #14557643 | 2 |
| C2×#11924467 | 2 |
| C2×#11924457 | 2 |
| C2×#11924456 | 2 |
| C2×#11924447 | 2 |
| C2×C4×D4×C37 | 2 |
| C2×#442 | 37 |