Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
280 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22562021 | C2 | semidirect |
| 3. #22558243 | C2 | semidirect |
| 4. #22558241 | C2 | semidirect |
| 5. C67×#2165 | C2 | semidirect |
| 125. #2165 | D67 | semidirect |
| 128. C67 | #11917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570610 | 2 |
| #22562021 | 2 |
| #22558243 | 2 |
| #22558241 | 2 |
| C67×#2165 | 2 |
| #11917 | 67 |