Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
464 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 162 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×#11924624 | C2 | semidirect |
| 2. C2×#11924623 | C2 | semidirect |
| 3. #14558578 | C2 | direct (N × H) |
| 4. C2×#11924607 | C2 | semidirect |
| 5. C2×#11924601 | C2 | semidirect |
| 6. C2×#11924600 | C2 | semidirect |
| 7. C2×#11924590 | C2 | semidirect |
| 10. #11924624 | C22 | semidirect |
| 12. #11924623 | C22 | semidirect |
| 21. #11924607 | C22 | semidirect |
| 22. #11924601 | C22 | semidirect |
| 23. #11924600 | C22 | semidirect |
| 24. #11924590 | C22 | semidirect |
| 27. #11924557 | C4 | semidirect |
| 29. C2×#10596942 | C4 | semidirect |
| 30. C2×#10596930 | C4 | semidirect |
| 31. C2×#10596939 | C4 | semidirect |
| 33. C2×SD16×C37 | C4 | semidirect |
| 68. SD16×C37 | C2×C4 | semidirect |
| 70. #10596942 | C2×C4 | semidirect |
| 71. #10596939 | C2×C4 | semidirect |
| 73. #10596930 | C2×C4 | semidirect |
| 128. C2×C37 | #444 | semidirect |
| 141. C37 | C2×#444 | semidirect |
| 148. C2×SD16 | #3866 | semidirect |
| 187. SD16 | C2×#3866 | semidirect |
| 263. C2 | #14558578 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924624 | 2 |
| C2×#11924623 | 2 |
| #14558578 | 2 |
| C2×#11924607 | 2 |
| C2×#11924601 | 2 |
| C2×#11924600 | 2 |
| C2×#11924590 | 2 |
| C2×#11924557 | 2 |
| C2×#444 | 37 |