Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 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. C4⋊Q8×D37 | C2 | semidirect |
| 3. #14557828 | C2 | semidirect |
| 4. #14557824 | C2 | semidirect |
| 5. #14557820 | C2 | semidirect |
| 6. #14557816 | C2 | semidirect |
| 7. #14557812 | C2 | semidirect |
| 8. #14557574 | C2 | semidirect |
| 9. #14557555 | C2 | semidirect |
| 11. C37×#477 | C2 | semidirect |
| 46. #10596966 | Q8 | semidirect |
| 86. Q8×C37 | C2×Q8 | semidirect |
| 100. D148 | C2×Q8 | semidirect |
| 141. #477 | D37 | semidirect |
| 149. C37 | #3079 | semidirect |
| 226. Q8 | Q8×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D37 | 2 |
| C4×#10596966 | 2 |
| #14557828 | 2 |
| #14557824 | 2 |
| #14557820 | 2 |
| #14557816 | 2 |
| #14557812 | 2 |
| #14557574 | 2 |
| #14557555 | 2 |
| #14557533 | 2 |
| C37×#477 | 2 |
| #3079 | 37 |