Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22561150 | C2 | semidirect |
| 5. #22558104 | C2 | semidirect |
| 6. #22558053 | C2 | semidirect |
| 7. C67×#1487 | C2 | semidirect |
| 92. C2×C67⋊C8 | SD16 | semidirect |
| 190. #1487 | D67 | semidirect |
| 193. C67 | #9047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570240 | 2 |
| #22568926 | 2 |
| #22561150 | 2 |
| #22558856 | 2 |
| #22558104 | 2 |
| #22558053 | 2 |
| C67×#1487 | 2 |
| #9047 | 67 |