Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
812 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 101 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×#16863537 | C2 | semidirect |
| 3. #22563867 | C2 | semidirect |
| 4. #22561045 | C2 | semidirect |
| 5. #22560145 | C2 | semidirect |
| 6. #22558778 | C2 | semidirect |
| 7. C67×#1282 | C2 | semidirect |
| 249. #1282 | D67 | semidirect |
| 250. C67 | #9948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570960 | 2 |
| C2×#16863537 | 2 |
| #22563867 | 2 |
| #22561045 | 2 |
| #22560145 | 2 |
| #22558778 | 2 |
| C67×#1282 | 2 |
| #9948 | 67 |