Finite Group DatabasebetaFinite Group DatabasebetaOrder 4672.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
|---|---|---|
| 2. #14556580 | C2 | semidirect |
| 3. D4×Dic73 | C2 | semidirect |
| 4. #14556520 | C2 | semidirect |
| 5. #14556515 | C2 | semidirect |
| 6. #14556513 | C2 | semidirect |
| 7. C2×SD16×C73 | C2 | semidirect |
| 55. C73 | #463 | semidirect |
| 57. C2×SD16 | D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924013 | 2 |
| #14556580 | 2 |
| D4×Dic73 | 2 |
| #14556520 | 2 |
| #14556515 | 2 |
| #14556513 | 2 |
| C2×SD16×C73 | 2 |
| #463 | 73 |