Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
384 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 124 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×C8×#3866 | C2 | semidirect |
| 4. (C2×#3866)⋊C8 | C2 | semidirect |
| 7. C2×D37⋊C8 | C4 | semidirect |
| 10. C22×#64438 | C4 | semidirect |
| 17. C22⋊#64436 | C4 | semidirect |
| 18. #11924448 | C4 | semidirect |
| 19. C22⋊C8×C37 | C4 | semidirect |
| 30. C22⋊#3866 | C8 | semidirect |
| 51. C2×#3866 | C2×C8 | semidirect |
| 66. #64438 | C22⋊C4 | semidirect |
| 71. C22×C37 | C4×C8 | semidirect |
| 76. C2×D37 | C4×C8 | semidirect |
| 98. C37 | C8×C22⋊C4 | semidirect |
| 110. C22⋊C8 | #3866 | semidirect |
| 171. C22 | C8×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D37⋊C8 | 2 |
| C2×C8×#3866 | 2 |
| C4×C22⋊#3866 | 2 |
| (C2×#3866)⋊C8 | 2 |
| C22⋊C8×D37 | 2 |
| C8×C22⋊C4 | 37 |