Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
472 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 472 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. #14558577 | C2 | direct (N × H) |
| 3. C2×#11924607 | C2 | semidirect |
| 4. C2×#11924601 | C2 | semidirect |
| 5. C2×C8×#3866 | C2 | semidirect |
| 8. #11924624 | C22 | semidirect |
| 14. #11924607 | C22 | semidirect |
| 15. #11924601 | C22 | semidirect |
| 16. C8×#3866 | C22 | semidirect |
| 18. #11924559 | C4 | semidirect |
| 20. C2×#10596941 | C4 | semidirect |
| 21. C2×D296 | C4 | semidirect |
| 23. C2×Q16×C37 | C4 | semidirect |
| 45. Q16×C37 | C2×C4 | semidirect |
| 47. #10596941 | C2×C4 | semidirect |
| 49. D296 | C2×C4 | semidirect |
| 89. C2×C37 | #443 | semidirect |
| 100. C37 | C2×#443 | semidirect |
| 104. C2×Q16 | #3866 | semidirect |
| 128. Q16 | C2×#3866 | semidirect |
| 185. C2 | #14558577 | 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 |
| #14558577 | 2 |
| C2×#11924607 | 2 |
| C2×#11924601 | 2 |
| C2×C8×#3866 | 2 |
| C2×#11924559 | 2 |
| C2×#443 | 37 |