Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
7034 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 7034 conjugacy classes of subgroups — too many to draw. Only its 675 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. C25×Dic67 | C2 | semidirect |
| 3. C2×#16863273 | C2 | semidirect |
| 4. #22558431 | C2 | semidirect |
| 5. C2×#379×C67 | C2 | semidirect |
| 12. C2×#14524012 | C4 | semidirect |
| 14. C22×(C2×D67)⋊C4 | C22 | semidirect |
| 16. C2×C67⋊#95 | C22 | semidirect |
| 25. C22×C22⋊D67 | C2×C4 | semidirect |
| 31. C23×Dic67 | D4 | semidirect |
| 37. C2×C22⋊Dic67 | C2×C4 | semidirect |
| 54. C23×D67 | C22×C4 | semidirect |
| 71. C22×Dic67 | C22×C4 | semidirect |
| 83. C24×C67 | C22⋊C4 | semidirect |
| 135. C2×Dic67 | #120 | semidirect |
| 143. C22×C67 | #386 | semidirect |
| 170. C2×#379 | D67 | semidirect |
| 172. C67 | #14694 | semidirect |
| 230. C24 | (C2×D67)⋊C4 | semidirect |
| 315. C22 | #16863273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×Dic67 | 2 |
| C22×#14524012 | 2 |
| C2×#16863273 | 2 |
| #22558431 | 2 |
| C2×#379×C67 | 2 |
| #14694 | 67 |