Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 79 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. #14558299 | C2 | semidirect |
| 3. #14557515 | C2 | semidirect |
| 4. C2×#11924453 | C2 | semidirect |
| 5. #14557305 | C2 | semidirect |
| 6. #14557304 | C2 | semidirect |
| 7. C2×#100×C37 | C2 | semidirect |
| 46. M16×C37 | D4 | semidirect |
| 56. #10596934 | D4 | semidirect |
| 119. C2×#100 | D37 | semidirect |
| 122. C37 | #1914 | semidirect |
| 166. M16 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558299 | 2 |
| #14558100 | 2 |
| #14557515 | 2 |
| C2×#11924453 | 2 |
| #14557305 | 2 |
| #14557304 | 2 |
| C2×#100×C37 | 2 |
| #1914 | 37 |