Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 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. #14558204 | C2 | semidirect |
| 2. #14557881 | C2 | semidirect |
| 3. #14557857 | C2 | semidirect |
| 4. #14557825 | C2 | semidirect |
| 5. #14557767 | C2 | semidirect |
| 6. #14557728 | C2 | semidirect |
| 7. #14557676 | C2 | semidirect |
| 8. C4×#10596940 | C2 | semidirect |
| 9. D4×#64436 | C2 | semidirect |
| 10. #14557527 | C2 | semidirect |
| 11. C37×#555 | C2 | semidirect |
| 133. #555 | D37 | semidirect |
| 144. C37 | #3305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558204 | 2 |
| #14557881 | 2 |
| #14557857 | 2 |
| #14557825 | 2 |
| #14557767 | 2 |
| #14557728 | 2 |
| #14557676 | 2 |
| C4×#10596940 | 2 |
| D4×#64436 | 2 |
| #14557527 | 2 |
| C37×#555 | 2 |
| #3305 | 37 |