Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22561830 | C2 | semidirect |
| 3. #22558193 | C2 | semidirect |
| 4. C67×#1812 | C2 | semidirect |
| 5. C22×D536 | C4 | semidirect |
| 8. #16863649 | C4 | semidirect |
| 12. #16863434 | C4 | semidirect |
| 15. #16863178 | C22 | semidirect |
| 19. H(3,ℤ/4)×C67 | C22 | semidirect |
| 153. #1812 | D67 | semidirect |
| 155. C67 | #11868 | semidirect |
| 170. H(3,ℤ/4) | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569857 | 2 |
| #22561830 | 2 |
| #22558193 | 2 |
| C67×#1812 | 2 |
| #11868 | 67 |