Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
578 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 578 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 |
| 4. #14543603 | C2 | semidirect |
| 38. #10587632 | C8 | semidirect |
| 61. C2×Q8×C17 | C2×C8 | semidirect |
| 99. C4⋊Dic17 | C2×C8 | semidirect |
| 250. C17 | #7589 | semidirect |
| 255. C2×Q8 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544641 | 2 |
| #14544445 | 2 |
| #14543604 | 2 |
| #14543603 | 2 |
| C4×#10587632 | 2 |
| #7589 | 17 |