Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 57 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×#11924477 | C2 | semidirect |
| 3. #14557769 | C2 | semidirect |
| 4. #14557337 | C2 | semidirect |
| 5. #14557334 | C2 | semidirect |
| 6. C22⋊#10596925 | C2 | semidirect |
| 7. C2×#135×C37 | C2 | semidirect |
| 33. Q16×C37 | D4 | semidirect |
| 36. D8×C37 | D4 | semidirect |
| 90. C2×#135 | D37 | semidirect |
| 97. C37 | #2186 | semidirect |
| 123. Q16 | C22⋊D37 | semidirect |
| 128. D8 | 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×#11924477 | 2 |
| #14557769 | 2 |
| #14557337 | 2 |
| #14557334 | 2 |
| C22⋊#10596925 | 2 |
| C2×#135×C37 | 2 |
| #2186 | 37 |