Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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×#11924479 | C2 | semidirect |
| 2. C2×D592 | C2 | semidirect |
| 3. C2×#11924477 | C2 | semidirect |
| 4. #14557918 | C2 | semidirect |
| 5. #14557908 | C2 | semidirect |
| 6. #14557308 | C2 | semidirect |
| 7. C2×SD32×C37 | C2 | semidirect |
| 42. C16×C37 | D4 | semidirect |
| 43. #10596925 | D4 | semidirect |
| 80. C2×SD32 | D37 | semidirect |
| 86. C37 | #2250 | semidirect |
| 122. C16 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924479 | 2 |
| C2×D592 | 2 |
| C2×#11924477 | 2 |
| #14557918 | 2 |
| #14557908 | 2 |
| #14557308 | 2 |
| C2×SD32×C37 | 2 |
| #2250 | 37 |