Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 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. #14558261 | C2 | semidirect |
| 2. #14557887 | C2 | semidirect |
| 4. #14557833 | C2 | semidirect |
| 5. #14557818 | C2 | semidirect |
| 6. #14557752 | C2 | semidirect |
| 8. Q8×#64436 | C2 | semidirect |
| 9. C4×#10596942 | C2 | semidirect |
| 10. C4×#10596940 | C2 | semidirect |
| 129. C37 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558261 | 2 |
| #14557887 | 2 |
| #14557879 | 2 |
| #14557833 | 2 |
| #14557818 | 2 |
| #14557752 | 2 |
| #14557730 | 2 |
| Q8×#64436 | 2 |
| C4×#10596942 | 2 |
| C4×#10596940 | 2 |
| C37×#559 | 2 |
| #3365 | 37 |