Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
772 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 772 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×D37⋊M16 | C2 | semidirect |
| 2. C2×#11924615 | C2 | semidirect |
| 3. #14558532 | C2 | direct (N × H) |
| 4. C2×#11924601 | C2 | semidirect |
| 6. C2×#10596953 | C22 | semidirect |
| 8. D37⋊M16 | C22 | semidirect |
| 12. #11924615 | C22 | semidirect |
| 15. C2×C4×#3866 | C22 | semidirect |
| 16. #11924601 | C22 | semidirect |
| 21. C2×#10596966 | C4 | semidirect |
| 22. C2×#10596966 | C4 | semidirect |
| 26. C22×D148 | C4 | semidirect |
| 29. C22×Q8×C37 | C4 | semidirect |
| 36. C2×Q8×C37 | C2×C4 | semidirect |
| 48. #10596966 | C2×C4 | semidirect |
| 57. C2×D148 | C2×C4 | semidirect |
| 75. C4×#3866 | C23 | semidirect |
| 77. #10596953 | C23 | semidirect |
| 146. C2×C37 | #421 | semidirect |
| 157. C37 | C2×#421 | semidirect |
| 166. C22×Q8 | #3866 | semidirect |
| 197. C2×Q8 | C2×#3866 | semidirect |
| 301. C2 | #14558532 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D37⋊M16 | 2 |
| C2×#11924615 | 2 |
| #14558532 | 2 |
| C2×#11924601 | 2 |
| C22×#10596966 | 2 |
| C2×#421 | 37 |