Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
618 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 618 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 |
|---|---|---|
| 1. #22569238 | C2 | semidirect |
| 3. #22558776 | C2 | semidirect |
| 4. #22558087 | C2 | semidirect |
| 5. C67×#1799 | C2 | semidirect |
| 12. #16863326 | C4 | semidirect |
| 13. #16863321 | C4 | semidirect |
| 14. #16863313 | C4 | semidirect |
| 15. #16863305 | C4 | semidirect |
| 44. C22⋊(C67⋊C8) | D4 | semidirect |
| 218. #1799 | D67 | semidirect |
| 221. C67 | #9386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569238 | 2 |
| #22565165 | 2 |
| #22558776 | 2 |
| #22558087 | 2 |
| C67×#1799 | 2 |
| #9386 | 67 |