Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11924558 | C2 | semidirect |
| 2. #14557963 | C2 | direct (N × H) |
| 3. C2×#11924482 | C2 | semidirect |
| 4. C2×#11924480 | C2 | semidirect |
| 5. C2×#11924479 | C2 | semidirect |
| 6. C2×#11924477 | C2 | semidirect |
| 7. C22×#10596925 | C2 | semidirect |
| 8. C2×#135×C37 | C2 | semidirect |
| 11. #11924558 | C22 | semidirect |
| 15. #11924482 | C22 | semidirect |
| 16. #11924480 | C22 | semidirect |
| 17. #11924479 | C22 | semidirect |
| 18. #11924477 | C22 | semidirect |
| 21. C2×#10596925 | C22 | semidirect |
| 24. #135×C37 | C22 | semidirect |
| 97. C2×C37 | #508 | semidirect |
| 101. C2×#135 | D37 | semidirect |
| 108. C37 | C2×#508 | semidirect |
| 114. #135 | C2×D37 | semidirect |
| 197. C2 | #14557963 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924558 | 2 |
| #14557963 | 2 |
| C2×#11924482 | 2 |
| C2×#11924480 | 2 |
| C2×#11924479 | 2 |
| C2×#11924477 | 2 |
| C22×#10596925 | 2 |
| C2×#135×C37 | 2 |
| C2×#508 | 37 |