Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
566 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 121 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×#16863198 | C2 | semidirect |
| 3. C2×#16863198 | C2 | semidirect |
| 4. #22560942 | C2 | semidirect |
| 5. C67×#1374 | C2 | semidirect |
| 37. #14523977 | D4 | semidirect |
| 154. #1374 | D67 | semidirect |
| 155. C67 | #13407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863773 | 2 |
| C2×#16863198 | 2 |
| #22560942 | 2 |
| C67×#1374 | 2 |
| #13407 | 67 |