Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
362 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 362 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. #14531040 | C2 | semidirect |
| 3. #14530830 | C2 | semidirect |
| 4. #14528154 | C2 | semidirect |
| 5. #14526831 | C2 | semidirect |
| 6. #14526746 | C2 | semidirect |
| 7. C17×Q8⋊C16 | C2 | semidirect |
| 94. Q8×C17 | SD32 | semidirect |
| 126. Q8⋊C16 | D17 | semidirect |
| 195. C17 | #12332 | semidirect |
| 237. Q8 | #10587471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541759 | 2 |
| #14531040 | 2 |
| #14530830 | 2 |
| #14528154 | 2 |
| #14526831 | 2 |
| #14526746 | 2 |
| C17×Q8⋊C16 | 2 |
| #12332 | 17 |