Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
460 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. C4×#14523976 | C2 | semidirect |
| 4. #22558708 | C2 | semidirect |
| 6. #22558496 | C2 | semidirect |
| 7. C67×#1986 | C2 | semidirect |
| 9. #16863792 | C4 | semidirect |
| 10. #16863770 | C4 | semidirect |
| 11. #16863746 | C4 | semidirect |
| 12. #16863744 | C4 | semidirect |
| 163. C67⋊C8 | #104 | semidirect |
| 192. #1986 | D67 | semidirect |
| 198. C67 | #9722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570769 | 2 |
| #22561128 | 2 |
| C4×#14523976 | 2 |
| #22558708 | 2 |
| #22558703 | 2 |
| #22558496 | 2 |
| C67×#1986 | 2 |
| #9722 | 67 |