Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 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. Q8×Dic74 | C2 | semidirect |
| 3. #14557883 | C2 | semidirect |
| 5. #14557818 | C2 | semidirect |
| 7. #14557740 | C2 | semidirect |
| 8. #14557664 | C2 | semidirect |
| 9. #14557638 | C2 | semidirect |
| 128. C37 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic74 | 2 |
| #14557892 | 2 |
| #14557883 | 2 |
| #14557823 | 2 |
| #14557818 | 2 |
| #14557752 | 2 |
| #14557740 | 2 |
| #14557664 | 2 |
| #14557638 | 2 |
| C4×#10596940 | 2 |
| C37×#556 | 2 |
| #3369 | 37 |