Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
536 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#16863732 | C2 | semidirect |
| 4. #22560287 | C2 | semidirect |
| 5. #22558572 | C2 | semidirect |
| 7. C67×#1298 | C2 | semidirect |
| 200. #1298 | D67 | semidirect |
| 201. C67 | #9994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571016 | 2 |
| C2×#16863732 | 2 |
| C2×#16863710 | 2 |
| #22560287 | 2 |
| #22558572 | 2 |
| #22558568 | 2 |
| C67×#1298 | 2 |
| #9994 | 67 |