Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
452 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22569376 | C2 | semidirect |
| 3. #22561040 | C2 | semidirect |
| 4. #22558696 | C2 | semidirect |
| 5. #22558679 | C2 | semidirect |
| 6. #22558103 | C2 | semidirect |
| 7. C67×#1299 | C2 | semidirect |
| 10. #16863805 | C4 | semidirect |
| 11. #16863785 | C4 | semidirect |
| 12. #16863761 | C4 | semidirect |
| 13. #16863756 | C4 | semidirect |
| 222. #1299 | D67 | semidirect |
| 223. C67 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570804 | 2 |
| #22569376 | 2 |
| #22561040 | 2 |
| #22558696 | 2 |
| #22558679 | 2 |
| #22558103 | 2 |
| C67×#1299 | 2 |
| #8997 | 67 |