Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
498 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#16863748 | C2 | semidirect |
| 4. #22558895 | C2 | semidirect |
| 6. #22558047 | C2 | semidirect |
| 7. C67×#1997 | C2 | semidirect |
| 170. #1997 | D67 | semidirect |
| 174. C67 | #10156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571337 | 2 |
| #22570603 | 2 |
| C2×#16863748 | 2 |
| #22558895 | 2 |
| #22558659 | 2 |
| #22558047 | 2 |
| C67×#1997 | 2 |
| #10156 | 67 |