Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924567 | C2 | semidirect |
| 2. C22×#10596941 | C2 | semidirect |
| 4. #14557755 | C2 | semidirect |
| 5. #14557733 | C2 | semidirect |
| 6. #14557560 | C2 | semidirect |
| 7. #14557537 | C2 | semidirect |
| 8. #14557527 | C2 | semidirect |
| 9. C37×#519 | C2 | semidirect |
| 13. C2×#10596942 | C22 | semidirect |
| 16. C2×#10596941 | C22 | semidirect |
| 23. C4⋊#64436 | C22 | semidirect |
| 24. #11924459 | C22 | semidirect |
| 26. #11924456 | C22 | semidirect |
| 29. C4×Q8×C37 | C22 | semidirect |
| 36. C2×Q8×C37 | D4 | semidirect |
| 120. #519 | D37 | semidirect |
| 126. C37 | #3043 | semidirect |
| 142. C4×Q8 | C2×D37 | semidirect |
| 156. C2×Q8 | D148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924567 | 2 |
| C22×#10596941 | 2 |
| #14558102 | 2 |
| #14557755 | 2 |
| #14557733 | 2 |
| #14557560 | 2 |
| #14557537 | 2 |
| #14557527 | 2 |
| C37×#519 | 2 |
| #3043 | 37 |