Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 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. C22×#10596942 | C2 | semidirect |
| 3. #14557912 | C2 | semidirect |
| 4. #14557772 | C2 | semidirect |
| 5. #14557743 | C2 | semidirect |
| 6. #14557740 | C2 | semidirect |
| 7. #14557689 | C2 | semidirect |
| 8. #14557688 | C2 | semidirect |
| 9. C4×#10596942 | C2 | semidirect |
| 71. #10596942 | D4 | direct (N × H) |
| 88. D4×C37 | Q16 | semidirect |
| 113. C22×C37 | C2×Q16 | semidirect |
| 120. C4×C37 | C2×Q16 | semidirect |
| 142. C37 | D4×Q16 | semidirect |
| 224. D4 | #10596942 | direct (N × H) |
| 244. C22 | C2×#10596942 | semidirect |
| 254. C4 | C2×#10596942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596942 | 2 |
| D4×Dic74 | 2 |
| #14557912 | 2 |
| #14557772 | 2 |
| #14557743 | 2 |
| #14557740 | 2 |
| #14557689 | 2 |
| #14557688 | 2 |
| C4×#10596942 | 2 |
| D4×#64436 | 2 |
| D4×Q8×C37 | 2 |
| D4×Q16 | 37 |