Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
760 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 197 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. C22×#10596939 | C2 | semidirect |
| 2. C2×#11924533 | C2 | semidirect |
| 3. #14557909 | C2 | direct (N × H) |
| 4. C2×C4×#64436 | C2 | semidirect |
| 5. C2×#127×C37 | C2 | semidirect |
| 9. C2×#10596939 | C22 | semidirect |
| 12. #11924533 | C22 | semidirect |
| 13. C4×#64436 | C22 | semidirect |
| 17. #127×C37 | C22 | semidirect |
| 36. C2×#64436 | D4 | semidirect |
| 48. C2×C4×C37 | D8 | semidirect |
| 56. #64436 | C2×D4 | semidirect |
| 67. C4×C37 | C2×D8 | semidirect |
| 71. C2×C37 | #493 | semidirect |
| 77. C2×#127 | D37 | semidirect |
| 80. C37 | C2×#493 | semidirect |
| 91. #127 | C2×D37 | semidirect |
| 126. C2×C4 | #10596939 | semidirect |
| 142. C4 | C2×#10596939 | semidirect |
| 146. C2 | #14557909 | 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×#11924533 | 2 |
| #14557909 | 2 |
| C2×C4×#64436 | 2 |
| C2×#127×C37 | 2 |
| C2×#493 | 37 |