Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
444 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. #14543993 | C2 | semidirect |
| 4. C8×#63247 | C2 | semidirect |
| 5. #14543668 | C2 | semidirect |
| 6. #14543668 | C2 | semidirect |
| 257. C17 | #8245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544287 | 2 |
| #14544238 | 2 |
| #14543993 | 2 |
| C8×#63247 | 2 |
| #14543668 | 2 |
| #14537494 | 2 |
| #8245 | 17 |