Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 105 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. #14533783 | C2 | semidirect |
| 3. #14527453 | C2 | semidirect |
| 4. #14527279 | C2 | semidirect |
| 5. #14527179 | C2 | semidirect |
| 6. #14526685 | C2 | semidirect |
| 7. C17×#3037 | C2 | semidirect |
| 90. C2×Q8×C17 | D8 | semidirect |
| 196. #3037 | D17 | semidirect |
| 305. C17 | #10242 | semidirect |
| 317. C2×Q8 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539699 | 2 |
| #14533783 | 2 |
| #14527453 | 2 |
| #14527279 | 2 |
| #14527179 | 2 |
| #14526685 | 2 |
| C17×#3037 | 2 |
| #10242 | 17 |