Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
486 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22558972 | C2 | semidirect |
| 3. #22558256 | C2 | semidirect |
| 4. C67×#2163 | C2 | semidirect |
| 13. #16863149 | C22 | semidirect |
| 16. C4⋊C16×C67 | C22 | semidirect |
| 122. #2163 | D67 | semidirect |
| 125. C67 | #11964 | semidirect |
| 135. C4⋊C16 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863773 | 2 |
| #22558972 | 2 |
| #22558256 | 2 |
| C67×#2163 | 2 |
| #11964 | 67 |