Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
406 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22561981 | C2 | semidirect |
| 3. #22561925 | C2 | semidirect |
| 4. #22561838 | C2 | semidirect |
| 5. #22560252 | C2 | semidirect |
| 6. #22558324 | C2 | semidirect |
| 7. C67×#2140 | C2 | semidirect |
| 168. #2140 | D67 | semidirect |
| 172. C67 | #13404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863663 | 2 |
| #22561981 | 2 |
| #22561925 | 2 |
| #22561838 | 2 |
| #22560252 | 2 |
| #22558324 | 2 |
| C67×#2140 | 2 |
| #13404 | 67 |