Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
820 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 2. C2×#11924501 | C2 | semidirect |
| 3. #14557438 | C2 | semidirect |
| 4. #14557437 | C2 | semidirect |
| 10. C22×Dic74 | C4 | semidirect |
| 50. C22⋊Dic37 | Q8 | semidirect |
| 78. C2×Dic37 | C2×Q8 | semidirect |
| 81. Dic74 | C22⋊C4 | semidirect |
| 86. C22×C37 | C4×Q8 | semidirect |
| 114. C37 | Q8×C22⋊C4 | semidirect |
| 192. C22 | #11924501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic74 | 2 |
| C2×#11924501 | 2 |
| #14557438 | 2 |
| #14557437 | 2 |
| #14557391 | 2 |
| C22⋊C4×Dic37 | 2 |
| C4×C22⋊Dic37 | 2 |
| C37×#380 | 2 |
| Q8×C22⋊C4 | 37 |