Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
562 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16863794 | C2 | semidirect |
| 4. #22561198 | C2 | semidirect |
| 5. #22558880 | C2 | semidirect |
| 7. C67×#1278 | C2 | semidirect |
| 179. #1278 | D67 | semidirect |
| 180. C67 | #10172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571339 | 2 |
| C2×#16863794 | 2 |
| #22570668 | 2 |
| #22561198 | 2 |
| #22558880 | 2 |
| #22558661 | 2 |
| C67×#1278 | 2 |
| #10172 | 67 |