Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
506 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 137 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. #14545893 | C2 | semidirect |
| 3. #14545794 | C2 | semidirect |
| 21. C22×#3624 | C8 | semidirect |
| 30. C2×#63242 | C8 | semidirect |
| 36. C2×M16×C17 | C8 | semidirect |
| 37. C2×#63223 | C8 | semidirect |
| 40. C2×#63218 | C8 | semidirect |
| 41. C2×#63218 | C8 | semidirect |
| 178. C2×M16 | #3633 | semidirect |
| 203. C17 | #8156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545896 | 2 |
| #14545893 | 2 |
| #14545794 | 2 |
| C2×#11763775 | 2 |
| #8156 | 17 |