Finite Group DatabasebetaFinite Group DatabasebetaOrder 4672.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#11924028 | C2 | semidirect |
| 2. C2×#11924016 | C2 | semidirect |
| 3. C2×#11924013 | C2 | semidirect |
| 4. #14556514 | C2 | semidirect |
| 5. #14556511 | C2 | semidirect |
| 6. C22⋊#10596831 | C2 | semidirect |
| 7. #121×C73 | C2 | semidirect |
| 37. D292 | D4 | semidirect |
| 40. Dic146 | D4 | semidirect |
| 64. C73 | #449 | semidirect |
| 69. #121 | D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924028 | 2 |
| C2×#11924016 | 2 |
| C2×#11924013 | 2 |
| #14556514 | 2 |
| #14556511 | 2 |
| C22⋊#10596831 | 2 |
| #121×C73 | 2 |
| #449 | 73 |