Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11924564 | C2 | semidirect |
| 2. #14558083 | C2 | semidirect |
| 3. C2×C4×D148 | C2 | semidirect |
| 4. #14557749 | C2 | semidirect |
| 5. #14557739 | C2 | semidirect |
| 6. #14557729 | C2 | semidirect |
| 7. #14557535 | C2 | semidirect |
| 8. C37×#423 | C2 | semidirect |
| 15. #11924536 | C22 | semidirect |
| 16. #11924533 | C22 | semidirect |
| 17. #11924524 | C22 | semidirect |
| 28. #11924461 | C22 | semidirect |
| 29. #11924458 | C22 | semidirect |
| 32. C4⋊C8×C37 | C22 | semidirect |
| 33. C4⋊C8×C37 | C22 | semidirect |
| 46. C2×D148 | D4 | semidirect |
| 118. C4×C37 | AGL(1,ℤ/8) | semidirect |
| 136. #423 | D37 | semidirect |
| 138. C37 | #3036 | semidirect |
| 160. C4⋊C8 | C2×D37 | semidirect |
| 161. C4⋊C8 | C2×D37 | semidirect |
| 250. C4 | #11924564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924564 | 2 |
| #14558083 | 2 |
| C2×C4×D148 | 2 |
| #14557749 | 2 |
| #14557739 | 2 |
| #14557729 | 2 |
| #14557535 | 2 |
| C37×#423 | 2 |
| #3036 | 37 |