Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
214 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 71 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. #14528188 | C2 | semidirect |
| 4. #14526858 | C2 | semidirect |
| 5. #14526841 | C2 | semidirect |
| 7. Q8×C16×C17 | C2 | semidirect |
| 89. Q8×C16 | D17 | semidirect |
| 146. C17 | #12476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531008 | 2 |
| #14528188 | 2 |
| #14528144 | 2 |
| #14526858 | 2 |
| #14526841 | 2 |
| #14526831 | 2 |
| Q8×C16×C17 | 2 |
| #12476 | 17 |