Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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×#11924559 | C2 | semidirect |
| 2. #14558202 | C2 | semidirect |
| 3. #14557908 | C2 | semidirect |
| 4. #14557769 | C2 | semidirect |
| 5. #14557766 | C2 | semidirect |
| 6. #14557731 | C2 | semidirect |
| 7. #14557678 | C2 | semidirect |
| 8. #14557677 | C2 | semidirect |
| 9. Q16×Dic37 | C2 | semidirect |
| 10. C8×C22⋊D37 | C2 | semidirect |
| 11. C2×#135×C37 | C2 | semidirect |
| 59. Q16×C37 | D4 | semidirect |
| 134. Dic37 | #135 | semidirect |
| 144. C2×#135 | D37 | semidirect |
| 154. C37 | #3287 | semidirect |
| 202. Q16 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924559 | 2 |
| #14558202 | 2 |
| #14557908 | 2 |
| #14557769 | 2 |
| #14557766 | 2 |
| #14557731 | 2 |
| #14557678 | 2 |
| #14557677 | 2 |
| Q16×Dic37 | 2 |
| C8×C22⋊D37 | 2 |
| C2×#135×C37 | 2 |
| #3287 | 37 |