Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
322 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22561802 | C2 | semidirect |
| 3. #22558969 | C2 | semidirect |
| 4. #22558180 | C2 | semidirect |
| 5. #22558178 | C2 | semidirect |
| 6. #22558176 | C2 | semidirect |
| 7. C67×#1333 | C2 | semidirect |
| 157. #1333 | D67 | semidirect |
| 158. C67 | #11682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570777 | 2 |
| #22561802 | 2 |
| #22558969 | 2 |
| #22558180 | 2 |
| #22558178 | 2 |
| #22558176 | 2 |
| C67×#1333 | 2 |
| #11682 | 67 |