Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
434 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 111 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×#16863213 | C2 | semidirect |
| 5. #22561930 | C2 | semidirect |
| 6. #22560333 | C2 | semidirect |
| 7. C67×#2110 | C2 | semidirect |
| 13. #16863780 | C4 | semidirect |
| 14. #16863776 | C4 | semidirect |
| 174. #2110 | D67 | semidirect |
| 176. C67 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570703 | 2 |
| C2×#16863213 | 2 |
| #22561946 | 2 |
| #22561938 | 2 |
| #22561930 | 2 |
| #22560333 | 2 |
| C67×#2110 | 2 |
| #13216 | 67 |