Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
398 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 158 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. #14558583 | C2 | semidirect |
| 2. #14558565 | C2 | semidirect |
| 3. #14558561 | C2 | semidirect |
| 4. #14558556 | C2 | semidirect |
| 5. #14558550 | C2 | semidirect |
| 6. #14558536 | C2 | semidirect |
| 7. D37⋊(C4⋊C8) | C2 | semidirect |
| 76. D148 | M16 | semidirect |
| 116. C37 | #2990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558583 | 2 |
| #14558565 | 2 |
| #14558561 | 2 |
| #14558556 | 2 |
| #14558550 | 2 |
| #14558536 | 2 |
| D37⋊(C4⋊C8) | 2 |
| #14558001 | 2 |
| #2990 | 37 |