Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
296 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22562023 | C2 | semidirect |
| 3. #22561812 | C2 | semidirect |
| 4. #22558242 | C2 | semidirect |
| 5. #22558241 | C2 | semidirect |
| 6. #22558241 | C2 | semidirect |
| 7. C67×#1355 | C2 | semidirect |
| 149. #1355 | D67 | semidirect |
| 150. C67 | #11913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570858 | 2 |
| #22562023 | 2 |
| #22561812 | 2 |
| #22558242 | 2 |
| #22558241 | 2 |
| C67×#1355 | 2 |
| #11913 | 67 |