Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
554 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22561036 | C2 | semidirect |
| 3. C4×C8×Dic67 | C2 | semidirect |
| 4. #22558659 | C2 | semidirect |
| 5. C67×#1567 | C2 | semidirect |
| 7. #16863801 | C4 | semidirect |
| 8. #16863773 | C4 | semidirect |
| 9. #16863743 | C4 | semidirect |
| 66. C4×Dic67 | D8 | semidirect |
| 104. C8×C67 | #104 | semidirect |
| 131. #1567 | D67 | semidirect |
| 133. C67 | #9844 | semidirect |
| 233. C8 | #14523969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570788 | 2 |
| #22561036 | 2 |
| C4×C8×Dic67 | 2 |
| #22558659 | 2 |
| C67×#1567 | 2 |
| #9844 | 67 |