Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
676 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 122 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. #14543604 | C2 | semidirect |
| 56. C2×Q8×C17 | M16 | semidirect |
| 217. C17 | #7609 | semidirect |
| 226. C2×Q8 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544675 | 2 |
| #14544447 | 2 |
| #14543604 | 2 |
| C2×#11762716 | 2 |
| #7609 | 17 |