Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 3. #14557940 | C2 | semidirect |
| 4. #14557938 | C2 | semidirect |
| 5. #14557936 | C2 | semidirect |
| 6. #14557929 | C2 | semidirect |
| 9. C37×#498 | C2 | semidirect |
| 65. #10596929 | Q8 | semidirect |
| 86. C8×C37 | C2×Q8 | semidirect |
| 87. #64436 | C2×Q8 | semidirect |
| 113. #498 | D37 | semidirect |
| 116. C37 | #3165 | semidirect |
| 194. C8 | Q8×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558088 | 2 |
| C4⋊Q8×D37 | 2 |
| #14557940 | 2 |
| #14557938 | 2 |
| #14557936 | 2 |
| #14557929 | 2 |
| #14557572 | 2 |
| C4×#10596929 | 2 |
| C37×#498 | 2 |
| #3165 | 37 |