Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
562 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 562 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×#16863715 | C2 | semidirect |
| 3. C2×#16863710 | C2 | semidirect |
| 4. #22560287 | C2 | semidirect |
| 5. #22558568 | C2 | semidirect |
| 6. #22558568 | C2 | semidirect |
| 7. C67×#1298 | C2 | semidirect |
| 209. #1298 | D67 | semidirect |
| 210. C67 | #9992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571009 | 2 |
| C2×#16863715 | 2 |
| C2×#16863710 | 2 |
| #22560287 | 2 |
| #22558568 | 2 |
| C67×#1298 | 2 |
| #9992 | 67 |