Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
704 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22568655 | C2 | semidirect |
| 3. #22560150 | C2 | semidirect |
| 4. #22558778 | C2 | semidirect |
| 5. #22558568 | C2 | semidirect |
| 6. #22558114 | C2 | semidirect |
| 7. C67×#1298 | C2 | semidirect |
| 9. C2×#14524071 | C4 | semidirect |
| 10. C2×#14524071 | C4 | semidirect |
| 17. #16863398 | C4 | semidirect |
| 18. #16863398 | C4 | semidirect |
| 287. #1298 | D67 | semidirect |
| 288. C67 | #9347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569463 | 2 |
| #22568655 | 2 |
| #22560150 | 2 |
| #22558778 | 2 |
| #22558568 | 2 |
| #22558114 | 2 |
| C67×#1298 | 2 |
| #9347 | 67 |