Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
572 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 173 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×#11924558 | C2 | semidirect |
| 2. #14558083 | C2 | semidirect |
| 3. #14557917 | C2 | semidirect |
| 4. #14557913 | C2 | semidirect |
| 5. #14557910 | C2 | semidirect |
| 6. #14557906 | C2 | semidirect |
| 7. C2×C4×C8×C37 | C2 | semidirect |
| 31. C2×C8×C37 | D4 | semidirect |
| 65. C4×C37 | #135 | semidirect |
| 79. C2×C4×C8 | D37 | semidirect |
| 80. C37 | #3147 | semidirect |
| 107. C2×C8 | D148 | semidirect |
| 139. C4 | #11924558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924558 | 2 |
| #14558083 | 2 |
| #14557917 | 2 |
| #14557913 | 2 |
| #14557910 | 2 |
| #14557906 | 2 |
| C2×C4×C8×C37 | 2 |
| #3147 | 37 |