Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
712 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22568659 | C2 | semidirect |
| 3. #22560152 | C2 | semidirect |
| 4. #22558726 | C2 | semidirect |
| 5. #22558570 | C2 | semidirect |
| 6. #22558056 | C2 | semidirect |
| 7. C67×#1293 | C2 | semidirect |
| 9. C22×#11761617 | C4 | semidirect |
| 10. C22×D536 | C4 | semidirect |
| 19. C2×#14523968 | C4 | semidirect |
| 20. C2×#14523965 | C4 | semidirect |
| 287. #1293 | D67 | semidirect |
| 289. C67 | #9241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863543 | 2 |
| #22568659 | 2 |
| #22560152 | 2 |
| #22558726 | 2 |
| #22558570 | 2 |
| #22558056 | 2 |
| C67×#1293 | 2 |
| #9241 | 67 |