Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22569263 | C2 | semidirect |
| 3. #22558711 | C2 | semidirect |
| 4. C2×#16863129 | C2 | semidirect |
| 5. #22558568 | C2 | semidirect |
| 6. #22558097 | C2 | semidirect |
| 7. C67×#1280 | C2 | semidirect |
| 10. #16863732 | C4 | semidirect |
| 12. #16863715 | C4 | semidirect |
| 15. #16863549 | C4 | semidirect |
| 17. #16863532 | C4 | semidirect |
| 252. #1280 | D67 | semidirect |
| 253. C67 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570976 | 2 |
| #22569263 | 2 |
| #22558711 | 2 |
| C2×#16863129 | 2 |
| #22558568 | 2 |
| #22558097 | 2 |
| C67×#1280 | 2 |
| #9264 | 67 |