Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
458 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22561874 | C2 | semidirect |
| 3. #22558371 | C2 | semidirect |
| 4. C67×#2126 | C2 | semidirect |
| 7. C2×#14524040 | C4 | semidirect |
| 11. #16863770 | C4 | semidirect |
| 13. C4×#11761612 | C4 | semidirect |
| 15. #16863189 | C22 | semidirect |
| 19. #353×C67 | C22 | semidirect |
| 160. #2126 | D67 | semidirect |
| 162. C67 | #13585 | semidirect |
| 177. #353 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570662 | 2 |
| #22561874 | 2 |
| #22558371 | 2 |
| C67×#2126 | 2 |
| #13585 | 67 |