Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22558957 | C2 | semidirect |
| 3. #22558180 | C2 | semidirect |
| 4. #22558177 | C2 | semidirect |
| 5. C67×#2163 | C2 | semidirect |
| 138. #2163 | D67 | semidirect |
| 142. C67 | #11656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570779 | 2 |
| #22558957 | 2 |
| #22558180 | 2 |
| #22558177 | 2 |
| C67×#2163 | 2 |
| #11656 | 67 |