Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
498 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22561127 | C2 | semidirect |
| 3. #22558703 | C2 | semidirect |
| 4. #22558498 | C2 | semidirect |
| 5. C4×#106×C67 | C2 | semidirect |
| 7. #16863801 | C4 | semidirect |
| 8. #16863773 | C4 | semidirect |
| 9. #16863743 | C4 | semidirect |
| 117. C8×C67 | #104 | semidirect |
| 144. C4×#106 | D67 | semidirect |
| 147. C67 | #9721 | semidirect |
| 261. C8 | #14523971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570788 | 2 |
| #22561127 | 2 |
| #22558703 | 2 |
| #22558498 | 2 |
| C4×#106×C67 | 2 |
| #9721 | 67 |