Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14558338 | C2 | semidirect |
| 2. #14557974 | C2 | semidirect |
| 3. #14557968 | C2 | semidirect |
| 4. #14557963 | C2 | semidirect |
| 5. C2×#11924479 | C2 | semidirect |
| 6. #14557950 | C2 | semidirect |
| 7. C37×#578 | C2 | semidirect |
| 12. #11924482 | C22 | semidirect |
| 13. #11924480 | C22 | semidirect |
| 14. #11924479 | C22 | semidirect |
| 15. #11924479 | C22 | semidirect |
| 16. #11924477 | C22 | semidirect |
| 17. #11924476 | C22 | semidirect |
| 18. C2×#10596925 | C22 | semidirect |
| 21. #135×C37 | C22 | semidirect |
| 22. C2×Q16×C37 | C22 | semidirect |
| 75. #578 | D37 | semidirect |
| 82. C37 | #3416 | semidirect |
| 88. #135 | C2×D37 | semidirect |
| 89. C2×Q16 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558338 | 2 |
| #14557974 | 2 |
| #14557968 | 2 |
| #14557963 | 2 |
| C2×#11924479 | 2 |
| #14557950 | 2 |
| C37×#578 | 2 |
| #3416 | 37 |