Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
558 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 118 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. #14544728 | C2 | semidirect |
| 4. #14543627 | C2 | semidirect |
| 52. #10587505 | C8 | semidirect |
| 94. C22⋊Dic17 | C2×C8 | semidirect |
| 107. C23×C17 | C4⋊C8 | semidirect |
| 120. C2×C4×C17 | C4⋊C8 | semidirect |
| 231. C17 | #8851 | semidirect |
| 284. C23 | #10587544 | semidirect |
| 316. C2×C4 | #10587544 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545631 | 2 |
| #14544757 | 2 |
| #14544728 | 2 |
| #14543627 | 2 |
| #99×Dic17 | 2 |
| #8851 | 17 |