Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
594 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22561189 | C2 | semidirect |
| 5. #22558772 | C2 | semidirect |
| 6. #22558037 | C2 | semidirect |
| 7. C67×#1286 | C2 | semidirect |
| 11. #16863769 | C4 | semidirect |
| 12. #16863743 | C4 | semidirect |
| 32. #14524043 | C2×C4 | semidirect |
| 33. #14524043 | C2×C4 | semidirect |
| 64. C4×C8×C67 | C2×C4 | semidirect |
| 103. C4×Dic67 | SD16 | semidirect |
| 200. #1286 | D67 | semidirect |
| 202. C67 | #9295 | semidirect |
| 257. C4×C8 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571152 | 2 |
| #22562932 | 2 |
| #22561189 | 2 |
| #22558878 | 2 |
| #22558772 | 2 |
| #22558037 | 2 |
| C67×#1286 | 2 |
| #9295 | 67 |