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×#11924623 | C2 | semidirect |
| 2. #14558580 | C2 | direct (N × H) |
| 3. C2×#11924606 | C2 | semidirect |
| 4. C2×#11924600 | C2 | semidirect |
| 5. C2×#11924590 | C2 | semidirect |
| 8. #11924623 | C22 | semidirect |
| 14. #11924606 | C22 | semidirect |
| 15. #11924600 | C22 | semidirect |
| 16. #11924590 | C22 | semidirect |
| 18. #11924555 | C4 | semidirect |
| 20. C2×Dic148 | C4 | semidirect |
| 21. C2×#10596940 | C4 | semidirect |
| 23. C2×D8×C37 | C4 | semidirect |
| 44. D8×C37 | C2×C4 | semidirect |
| 46. #10596940 | C2×C4 | semidirect |
| 48. Dic148 | C2×C4 | semidirect |
| 88. C2×C37 | #444 | semidirect |
| 98. C37 | C2×#444 | semidirect |
| 104. C2×D8 | #3866 | semidirect |
| 128. D8 | C2×#3866 | semidirect |
| 181. C2 | #14558580 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924623 | 2 |
| #14558580 | 2 |
| C2×#11924606 | 2 |
| C2×#11924600 | 2 |
| C2×#11924590 | 2 |
| C2×#11924555 | 2 |
| C2×#444 | 37 |