Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14558188 | C2 | semidirect |
| 2. #14557885 | C2 | semidirect |
| 3. #14557874 | C2 | semidirect |
| 4. #14557820 | C2 | semidirect |
| 5. #14557760 | C2 | semidirect |
| 6. #14557738 | C2 | semidirect |
| 7. #14557676 | C2 | semidirect |
| 8. C4×#10596939 | C2 | semidirect |
| 9. D4×#64436 | C2 | semidirect |
| 10. #14557527 | C2 | semidirect |
| 11. C37×#555 | C2 | semidirect |
| 131. #555 | D37 | semidirect |
| 142. C37 | #3303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558188 | 2 |
| #14557885 | 2 |
| #14557874 | 2 |
| #14557820 | 2 |
| #14557760 | 2 |
| #14557738 | 2 |
| #14557676 | 2 |
| C4×#10596939 | 2 |
| D4×#64436 | 2 |
| #14557527 | 2 |
| C37×#555 | 2 |
| #3303 | 37 |