Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
874 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 874 conjugacy classes of subgroups — too many to draw. Only its 135 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×#16863211 | C2 | semidirect |
| 3. #22561936 | C2 | semidirect |
| 4. #22561830 | C2 | semidirect |
| 5. C67×#1813 | C2 | semidirect |
| 173. #1813 | D67 | semidirect |
| 174. C67 | #12744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864213 | 2 |
| C2×#16863211 | 2 |
| #22561936 | 2 |
| #22561830 | 2 |
| C67×#1813 | 2 |
| #12744 | 67 |