Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1492 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 754 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. #14558602 | C2 | semidirect |
| 2. #14558601 | C2 | semidirect |
| 3. #41×#3866 | C2 | semidirect |
| 4. C2×Q8×#3866 | C2 | semidirect |
| 14. #11924584 | C4 | semidirect |
| 15. #11924583 | C4 | semidirect |
| 18. 2−1+4×C37 | C4 | semidirect |
| 21. #41×C37 | C2×C4 | semidirect |
| 22. C2×Q8×C37 | C2×C4 | semidirect |
| 23. #10596966 | C2×C4 | semidirect |
| 24. Q8×D37 | C2×C4 | semidirect |
| 26. #10596964 | C2×C4 | semidirect |
| 28. #10596962 | C2×C4 | semidirect |
| 30. C2×Dic74 | C2×C4 | semidirect |
| 58. #3866 | 2−1+4 | direct (N × H) |
| 72. C37 | C4×2−1+4 | semidirect |
| 75. 2−1+4 | #3866 | direct (N × H) |
| 89. #41 | C2×#3866 | semidirect |
| 93. C2×Q8 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558602 | 2 |
| #14558601 | 2 |
| #41×#3866 | 2 |
| C2×Q8×#3866 | 2 |
| 2−1+4×D37 | 2 |
| C4×2−1+4 | 37 |