Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 202 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×#11924615 | C2 | semidirect |
| 2. #14558514 | C2 | direct (N × H) |
| 3. C2×#11924595 | C2 | semidirect |
| 6. #11924615 | C22 | semidirect |
| 10. #11924595 | C22 | semidirect |
| 14. C2×#10596966 | C4 | semidirect |
| 16. C22×D148 | C4 | semidirect |
| 18. C22×C4×D37 | C4 | semidirect |
| 20. C22×Q8×C37 | C4 | semidirect |
| 26. C2×Q8×C37 | C2×C4 | semidirect |
| 39. C2×D148 | C2×C4 | semidirect |
| 45. C2×C4×D37 | C2×C4 | semidirect |
| 108. C2×C37 | #410 | semidirect |
| 117. C37 | C2×#410 | semidirect |
| 123. C22×Q8 | #3866 | semidirect |
| 142. C2×Q8 | C2×#3866 | semidirect |
| 223. C2 | #14558514 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924615 | 2 |
| #14558514 | 2 |
| C2×#11924595 | 2 |
| C22×#10596966 | 2 |
| C2×#410 | 37 |