Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
456 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 149 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. #14558083 | C2 | semidirect |
| 2. #14557938 | C2 | semidirect |
| 3. #14557910 | C2 | semidirect |
| 4. #14557880 | C2 | semidirect |
| 5. #14557769 | C2 | semidirect |
| 6. C4×D296 | C2 | semidirect |
| 7. C2×C4×C8×C37 | C2 | semidirect |
| 50. C2×C4×C37 | D8 | semidirect |
| 65. C8×C37 | #41 | semidirect |
| 92. C2×C4×C8 | D37 | semidirect |
| 93. C37 | #3169 | semidirect |
| 143. C2×C4 | D296 | semidirect |
| 151. C8 | #10596962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558083 | 2 |
| #14557938 | 2 |
| #14557910 | 2 |
| #14557880 | 2 |
| #14557769 | 2 |
| C4×D296 | 2 |
| C2×C4×C8×C37 | 2 |
| #3169 | 37 |